Resolvi utilizando a lógica mesmo. Por exemplo: 7 elevado a potência 2 = 7 X 7 = 49, 5 elevado a segunda potência = 5 X 5 = 25, logo 49 - 25= 24, 7 X 5 = 35 e 7 + 5 =12.
Very easy to solve. No big formula required. X+Y = 12. XY=35. 35=35*1 or 17.5*2 or 7*5. First two are not suitable. So 7*5 =XY.. So X=7. Y=5. So 7*7=49. 5*5=25. 49-25=24. 7+5=12.
@@AshmanKhanna Not hit and run. Only some logic is applied. I applied the logic in case of XY=35 and got the value of X and Y. In competitive exams we do not have much time to solve these types of questions. Only logic should be applied for faster solutions.
Пусть (х+у)^2=а, возведем первое уравнение в квадрат (х+у)^2*(х-у)^2=576 а*(х^2+у^2+2ху-2ху-2ху)=576 В скобках мы прибавили и отняли 2ху а*((х+у)^2-4ху)=576 а*(а-140)=576 Дальнейшее просто
@@anime_pro_fan539 Я согласен, но так могут решить не все. Вообще это устно решается. х,у числа явно целые. 35 имеет два делителя 7 и 5 (1 и 35 не учитываем). Легко посчитать два решения (7,5) и (-7,-5) И есть ещё комплексное решение
@@user-ee7nw2rx9s ну я хз, как по мне с такой системой что ты написал решить смогут ещё меньше чем так как я написал, я такое решаю быстро, даже после титановый сетки в голове из-за перелома черепа, но сложные задачи и многое другое прокручиваются в голове медленнее чем раньше, хотя оно и понятно сломал себе череп из-за своей тупости и в ней шя титановая сетка
The question doesn’t tell you they’re natural numbers, of course you could guess get because it doesn’t make sense for them to be very complex, but “guessing numbers” is normally a no go for math Olympics
35²=25×49=1225 It's a small mistake, but in (x,y)=(5,7),(-5,-7), x and y are reversed, so I don't feel like squaring 35. There is an answer, but you can do it without squaring x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧y=35/x ⇔x²-(35 /x)²=24∧y=35/x ⇔x⁴-24x²-7²・5²=0∧y=35/x ⇔(x²-7²)(x²+5²)=0∧y=35/x ⇔(x ,y)=(7,5),(-7,5),(5i,-7i),(-5i,7i) Of course I didn't calculate 35². Well, there is a rule like 15²=2 25 25²=6 25 35²=12 25 45²= 20 25 55²=30 25 65²= 42 25, so if you know that, you can calculate it right away.
Simple trick, 35 number ki divisers are 1,5,7 and 35 numbers only. Next 1 square is 1 and 5 square is 25 and 7 square is 49. And 35 square is 1225 and this 1225 is big number. So, automatically 49-25 is 24. So required numbers are 7 and 5.
Math bukan tentang JAWABAN, tapi prosesnya. Manusia dikatakan MENGGUNAKAN LOGIKA jika mampu menjelaskan PROSES. Inilah sebabnya kenapa IQ ORANG INDONESIA RENDAH, karena hanya berorientasi pada HASIL. INDONESIA TIDAK MAJU karena warganya hanya ingin HASIL bukan proses.
@@haylonmi писать то надо но если устно просто нужно сказать ответ то достаточно сказать 7 и 5, а если, ну я то уже 2 года как школу закончил так что не могу сказать какие у вас учителя, но если учитель спросит ,,и это всё?" Значит учитель хочет от тебя ответ ±7 и ±5
After seeing the equations squaring both numbers then subtracting from get results in 24 multiplying x and get 35 makes x=7 y=5 adding them up results in 12
set u=x+y and v= x-y then u*v=24 but (x+y)^2-(x-y)^2=4*x*y=4*35 Therefore u^2-v^2=4*35, v^2=u^2-4*35. u^2*v^2=24^2 u^2*(u^2-4*35)=24^2 u^2-2*2*35*u^2=24^2 (u^2-2*35)^2=24^2+(2*35)^2=4*12^2+4*35^2 (u^2-2*35)^2=4*(12^2+35^2)=4*(35^2+12^2). but 36^2=(35+2)^2=35^2+2*2*35+2^2=35^2+140+4=35^2+12^2 Thus (u^2-2*35)^2=4*37^2 u^2=2*35+-2*37=2*(35+-37) u^2=2*(35+37)=144 or u^2=2*(-2)=-4
at 6:32 - x^2+y^2 = 5476 if you take roots, isn't everything already positive? How taking square roots from both sides gets you with +/-? Please explain...?
Another thing, even if the number are negative they are both negative, it's not possible for one to be negative and the other positive since xy=35. So the answer can be +/-12
Есть ощущение, что решить попроще можно было. А так... Как говорят у нас, в Африке, "пока одни изучают комплексные числа, другие в это время изучают автомат Калашникова" 😐
Math not about the answer but PROCESS. Every one can say 1 + 1 = 2, 1 x 2 =2, 4 ÷ 2 = 2, but can you explain how??? The code of computer program to explainted for 1 + 1 = 2 need 10 or more of line code. Explaint the process is real problem. If human just need answer than CALL GOD.
Is there any squared number that gives a negative result?, when we see (x+y) squared < 0 ( reject no more answer ) but you still have the next solution, your math level is too advanced, I don't know who taught you the basic knowledge, just let me know so I can tell that person to prove it to the world is the square of a negative number to receive the Nobel Prize in mathematics
here it’s impossible to say for sure if we take the + sign, because 12 can also be obtained by 4+8, 3+9, etc., but if we take xy, then it’s clear because 35 is only in the case of 7×5 and this fits everyone’s requirements, but with + you can already have a bunch of options, and if 7+5 doesn’t immediately come to mind, then you’ll try 2+10, 3+9, 4+8, 11+1, etc. even -2+14, but with xy=35 it’s immediately clear because everyone knows the multiplication table from the age of 7
What kind of number do the variables x and y denote?Is there any indication regarding the question, it should be mentioned while the solution is explained.,The question to be set in the Math Olympiad brings no credit.
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é: x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
This question is prepared in a way such that the answer could be obtained by doing prime factorisation of 35 , using any other ways is just dumb way of solving and a matter of waste of time
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é: x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
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ans. x=7. &. y=5 ,( no need to solve) so x+y=7+5=12.
L intéressant c est de faire la démonstration ,le résultat a peu d importance .
Not that simple
That's just sort of guessing!
35=7×5=>x=7 and y=5
No. The numbers might be negative too. (-7) and (-5).
(-7)×(-5)=35
2 2
(-7) - (-5) = 49-25 = 24
So, we need to solve.
Just looking at the factors of 35 it's clear that it must be +-7 and +-5, so +-12
Put x=35/y and substitute in the other equation you can get both x and y and then x+y
no u cant lol
x=35/y
35^2/y^ - y^2 = 24
y^4+24y^2 - 35 = 0 ----> quadratic eq.
y^2 = 49 or -25
y = +7 or -7
x = 35/y = +5 or -5
x+y = 12 or -12
Resolvi utilizando a lógica mesmo. Por exemplo: 7 elevado a potência 2 = 7 X 7 = 49, 5 elevado a segunda potência = 5 X 5 = 25, logo 49 - 25= 24, 7 X 5 = 35 e 7 + 5 =12.
Very easy to solve. No big formula required. X+Y = 12.
XY=35. 35=35*1 or 17.5*2 or 7*5. First two are not suitable. So 7*5 =XY..
So X=7. Y=5. So 7*7=49. 5*5=25. 49-25=24.
7+5=12.
Bro you have used hit and trial method but we should use proper identity or logic which is shown in video
@@AshmanKhanna
Not hit and run. Only some logic is applied. I applied the logic in case of XY=35 and got the value of X and Y. In competitive exams we do not have much time to solve these types of questions. Only logic should be applied for faster solutions.
Решение на сообразительность:
ХY=35 - первое, что приходит на ум 7×5
7 в квадрате =49
5 в квадрате = 25
49-25=24
7+5=12!
8:04 everything was perfect until you started looking for the sqrt, after that I got disappointed
Пусть (х+у)^2=а, возведем первое уравнение в квадрат
(х+у)^2*(х-у)^2=576
а*(х^2+у^2+2ху-2ху-2ху)=576
В скобках мы прибавили и отняли 2ху
а*((х+у)^2-4ху)=576
а*(а-140)=576
Дальнейшее просто
И ты усложнил как и автор ведь тут чисто на логике можно решить xy=35=>x=35/y либо y=35/x=>x=±7 и y=±5
@@anime_pro_fan539
Я согласен, но так могут решить не все. Вообще это устно решается.
х,у числа явно целые.
35 имеет два делителя 7 и 5 (1 и 35 не учитываем).
Легко посчитать два решения (7,5) и (-7,-5)
И есть ещё комплексное решение
@@user-ee7nw2rx9s ну я хз, как по мне с такой системой что ты написал решить смогут ещё меньше чем так как я написал, я такое решаю быстро, даже после титановый сетки в голове из-за перелома черепа, но сложные задачи и многое другое прокручиваются в голове медленнее чем раньше, хотя оно и понятно сломал себе череп из-за своей тупости и в ней шя титановая сетка
Or you could have just got it from xy=35 x=±7 y=±5 x+y=±12
😉
The question doesn’t tell you they’re natural numbers, of course you could guess get because it doesn’t make sense for them to be very complex, but “guessing numbers” is normally a no go for math Olympics
12(X7,Y5)
35²=25×49=1225
It's a small mistake, but in (x,y)=(5,7),(-5,-7), x and y are reversed, so I don't feel like squaring 35. There is an answer, but you can do it without squaring x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧y=35/x ⇔x²-(35 /x)²=24∧y=35/x ⇔x⁴-24x²-7²・5²=0∧y=35/x ⇔(x²-7²)(x²+5²)=0∧y=35/x ⇔(x ,y)=(7,5),(-7,5),(5i,-7i),(-5i,7i) Of course I didn't calculate 35². Well, there is a rule like 15²=2 25 25²=6 25 35²=12 25 45²= 20 25 55²=30 25 65²= 42 25, so if you know that, you can calculate it right away.
X e 7, y e 5 , x +y = 12
x=7,y=5
×=-7,y=-5
x+y=7+5=12
×+y=(-7)+(-5)=-12
Simple trick, 35 number ki divisers are 1,5,7 and 35 numbers only.
Next 1 square is 1 and 5 square is 25 and 7 square is 49. And 35 square is 1225 and this 1225 is big number.
So, automatically 49-25 is 24.
So required numbers are 7 and 5.
It's very easy 35, is divisible by only two numbers 7 and 5
So x is 7 and y is 5
XY=35
Factors of XYvalue 35 are 7 and 5
Then X + Y =, 7+5=12
Terlalu panjang..asal hafal kali2an cepat terjawab...x= 7 y=5
x + y = 12
Math bukan tentang JAWABAN, tapi prosesnya.
Manusia dikatakan MENGGUNAKAN LOGIKA jika mampu menjelaskan PROSES.
Inilah sebabnya kenapa IQ ORANG INDONESIA RENDAH, karena hanya berorientasi pada HASIL.
INDONESIA TIDAK MAJU karena warganya hanya ingin HASIL bukan proses.
how about x= -7 and y= -5
7and5
😅7 и 5. Моментально ❗
-7 и - 5 забыли
@@haylonmiну -7 и -5 не нужно говорить ведь это просто то же самое в отрицательном виде, ну а так да ±7 и ±5
@@anime_pro_fan539 нужно, это же тоже вариант ответа. Или, по-вашему, X² = 49 => x = ±7, то достаточно записать x = 7? Это не так.
@@haylonmi писать то надо но если устно просто нужно сказать ответ то достаточно сказать 7 и 5, а если, ну я то уже 2 года как школу закончил так что не могу сказать какие у вас учителя, но если учитель спросит ,,и это всё?" Значит учитель хочет от тебя ответ ±7 и ±5
xy = 35 = 35x1 or 7x5. Now (35+1)(35-1) = 1224 and (7+5)(7-5) = 24 . So …….
After seeing the equations squaring both numbers then subtracting from get results in 24 multiplying x and get 35 makes x=7 y=5 adding them up results in 12
24 в квадрате равно 496
Why are you not telling us the laws you applied and what's the application to real life situation?
Задание интересное!
Need simple tips
12
24 =12×2. X+y =12
=(7+5)(7-5)
X=7. y=5
X+ y=. 12
set u=x+y and v= x-y
then u*v=24
but
(x+y)^2-(x-y)^2=4*x*y=4*35
Therefore u^2-v^2=4*35, v^2=u^2-4*35.
u^2*v^2=24^2
u^2*(u^2-4*35)=24^2
u^2-2*2*35*u^2=24^2
(u^2-2*35)^2=24^2+(2*35)^2=4*12^2+4*35^2
(u^2-2*35)^2=4*(12^2+35^2)=4*(35^2+12^2).
but 36^2=(35+2)^2=35^2+2*2*35+2^2=35^2+140+4=35^2+12^2
Thus
(u^2-2*35)^2=4*37^2
u^2=2*35+-2*37=2*(35+-37)
u^2=2*(35+37)=144 or u^2=2*(-2)=-4
7 x 5 = 35. Por lo tanto 7 + 5=12
i ❤ Mathematics
at 6:32 - x^2+y^2 = 5476 if you take roots, isn't everything already positive? How taking square roots from both sides gets you with +/-? Please explain...?
Another thing, even if the number are negative they are both negative, it's not possible for one to be negative and the other positive since xy=35. So the answer can be +/-12
For example if we have to solve for x in x^2=49, then x will be +-7 but √49=+7 only
Wondraful
Thank you 🙏
Good luck sR❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Let
u = x + y,
v = x - у
Then
x² - y² = 24 => uv = 24 (1)
xy = 35 => u² - v² = 4*35 = 140 (2)
From (1)
v = 24/u (3)
Substitute (3) in (2)
u² - (24/u)² = 140
or
u⁴ - 24² = 140u²
or
u⁴ - 140u² - 24² = 0 (4)
From (4)
u²₁,₂ = [140 ± √(140² + 4*24²)] / 2 = [140 ± √(4² * (35² + 12²))] / 2 = [140 ± 4√(1369))] / 2 = [140 ± 4√(37²))] / 2 = 70 ± 2*37 = 70 ± 74
u²₁ = 144 => (x + y) = ±12
u²₂= -4 => (x + y) = ±2i
❤️❤️
Есть ощущение, что решить попроще можно было.
А так... Как говорят у нас, в Африке, "пока одни изучают комплексные числа, другие в это время изучают автомат Калашникова" 😐
Math not about the answer but PROCESS.
Every one can say 1 + 1 = 2, 1 x 2 =2, 4 ÷ 2 = 2, but can you explain how???
The code of computer program to explainted for 1 + 1 = 2 need 10 or more of line code.
Explaint the process is real problem.
If human just need answer than CALL GOD.
,12
암산해도x=±7,y=±5,
x+y=±12
First step is wrong because
(x+y)(x-y)=x2-y2-2xy
Решила в уме 5*7=35. И 49 - 25≠24
x =7 y= 5
x+y= 7+5=12
Simple 12
Solution is to be speed slow writing makes us irritation if u write like this is there any meaning plse explain
35 : 5 dhe 35:7
X= 5 ose x=7
Prova. X=7 dhey=5
x=7 y=5
-12,-2,2,12
Trivial x=7,y=5
But actual time to solve ->30 secs in any exams
X-7, y-5, 7+5=12
Is there any squared number that gives a negative result?, when we see (x+y) squared < 0 ( reject no more answer ) but you still have the next solution, your math level is too advanced, I don't know who taught you the basic knowledge, just let me know so I can tell that person to prove it to the world is the square of a negative number to receive the Nobel Prize in mathematics
The process is lengthy
Да это устная задача...
X+y=12
x + y = 7 + 5 = 12
X*y=35.
7*5=35.
7+5=12
இவ்வளவு மெதுவாக செய்தால் பிள்ளைகள் பார்க்க மாட்டார்கள்
Много лишнего,надо применять простую таблицу умножения.7•5= 35 и все!
35= 7×5=>x=7 and y=5 😑
X=7,Y=5
7+5=12
Simple salvation kora uchit.
Ответ 12,метод подстановки
Matematica trebuie sa simplifice lucrurile , nu să le complice! Doar dacă vrei să dovedesti ca sti toate formulele.
Hic x+y=12 est. Responsi.
Risposta : 7. e. 5.
Too lengthy just use brain
x = ±7; y = ±5
x + y = ±12
here it’s impossible to say for sure if we take the + sign, because 12 can also be obtained by 4+8, 3+9, etc., but if we take xy, then it’s clear because 35 is only in the case of 7×5 and this fits everyone’s requirements, but with + you can already have a bunch of options, and if 7+5 doesn’t immediately come to mind, then you’ll try 2+10, 3+9, 4+8, 11+1, etc. even -2+14, but with xy=35 it’s immediately clear because everyone knows the multiplication table from the age of 7
x+y=±12
What kind of number do the variables x and y denote?Is there any indication regarding the question, it should be mentioned while the solution is explained.,The question to be set in the Math Olympiad brings no credit.
38
Giải rườm rà vậy. X = 35/Y . Thay vào rồi giải phương trình bậc 2 thôi
Я за несколько секунд нашла ответ Х+У=12, Х=7, У=5
Х=7 , У=5 от 35-24=12
12 or -12
There are no factors other than 7x5 for 35
So answer must be 7 and 5
Silly question
Решаем в уме. х +у = 12.
12.
X=25,,,,y=1
Method.
O X equivale a 7 e o Y a 5
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é:
x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
7 + 5= 12
Why need to mention +_ even it is positive.
X=7 y=5 so x+y =12
Solution method is lengthy nd wrong
This question is prepared in a way such that the answer could be obtained by doing prime factorisation of 35 , using any other ways is just dumb way of solving and a matter of waste of time
There is an easiest way to solve it!!
X=35/y and replace
A resposta correta é 12
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é:
x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
Wrong solve.
Olympiad??? Is someone extracting the yellow water of hilarity ? ? I got this in 5 seconds and I openly admit to a full set of numbskull genes.
Полнейшая чушь.... Мой племянник 10 лет решил в уме за 20 секунд...Самый тупой препод...
Wrong method।
Eu resolvi de cabeça, xy=35, só 7×5=35.
Всё решается в уме по первой строчке все понятно.зачеи столько трудностей и писанины.кстати мне65
12
X+y=12
12
12
12
12
12
12
12