Japanese | Can you solve this ? | A Nice Math Olympiad Algebra Problem.
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- Опубликовано: 11 сен 2024
- This is an interesting question with amazing concepts!
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Multiply ab bc ca . We get a square, b square c square. So we get abc whole square. By way of this we get the value of abc. Then divide by the values of ab, bc, ca and get the value of a,b,c. Then just add and get the value of a + b + c. Simple
Simple in three steps🎉
This method is easier than your solution procedure sir.
a= √150 ; b=√(200/3); c=√600
a+b+c= 5√6 + 10√2/√3 + 10√6
=5/√6+10√6/3+10√6
= √6(5+10/3+10)
=√6(15+10/3)
=√6(55/3)
a+b+c = 55√6/3
Сравнив 1-ое и 2-ое видим, что с= 2а.
Из 3-его следует- 2а^=300; отсюда-а=5√6;с=10√6;в=20/√6; в итоге: а+в+с =55√6/3;Самое простое решение.
А сравнить зачем?
Вроде выражаем, подставляем - должно решаться элементарно (система для пятого класса школы).
LCM of (1,2,3)=6
6abc=6cx100=600c
3abc=3a×200=600a
2abc=2bx300=600b
Add 11abc=600(a+b+c)
ab×bc×ca=100x200x300
(abc)^2=(1000)^2×6
abc=1000√6
11x1000√6=600(a+b+c)
a+b+c=110/√6=(55√2)/√3
ruclips.net/video/TDFfjc00nvk/видео.html
Your method seems much simpler but I still had problems following it. Where can I go to practice your method?
@@joseeoliviero6078 How do you think about this method?
(3) / (1) gives c / b = 3 : 1
(2) / (1) gives c / a = 2 : 1
∴ a : b : c = 3k : 2k : 6k
By (1), 6k^2 = 100
∴ k^2 = 50/3
k = +- (5√2) / √3
Their sum equals 11k.
∴ a + b + c = +- (55√2) / √3
= +- 55√6 / 3
Done.
@@N_Kumar26 And you missed the negative solution
This type of question is asking in exam then you quickly make answer. You can practice your self like ab=400
bc=200
ca=800 find value of a^2+b^2+c^2
Here you tube link you could know more class wise questions and answers.
ruclips.net/video/TDFfjc00nvk/видео.html
Lengthy process,find a²b²c² first,then a,b,c ,add three
100+200+300=600
a+a+b+b+c+c=600
a+b+c. =300..very simple .and easy..Total letter =600..than.you take half..
Of Total letter equal 300..
It is too lengthy procedure
Erry puvvava nuvvu
After you got a^2 b^2 and c^2 you could radicalize both side and add the results. Before of you go a lot of steps but the video is good keep it up🎉
a=100,b=0 c=200
No need of formula
Yes directly we can do.
a+b+c also admits its negative value. With a b c negative.
c / b = 3 : 1
c / a = 2 : 1
∴ a : b : c = 3k : 2k : 6k
By (1), 6k^2 = 100
∴ k^2 = 50/3
k = +- (5√2) / √3
Their sum equals 11k.
∴ a + b + c = +- (55√2) / √3
= +- 55√6 / 3
Done.
Easiest solution
Hats off
simplest one.
1- ab = 100
2. bc = 200
3. ca = 300
1*2*3
ab*bc*ca = 100*200*300
(abc)^2 = 6000000
abc = (√ 6000000 ) = √ (6 * 1000000 ) = √6 * 1000 = 1000 √6
=>1 ab = 100 ,.abc = 1000 √6 , 100 * c = 1000 √6 , c = (1000 √6 ) / 100 = 10√6
=>2 bc = 200 , abc = 1000 √6 , 200 * a = 1000 √6 , a = (1000 √6) / 200 = 5√6
=>3 ca = 300 , abc = 1000 √6 , 300 * b = 1000 √6 , b = (1000 √6 ) / 300 = (1000/300) * √6 = (10/3) * √6
a+b+c = 10√6 + 5√6 + ((10/3) * √6) = (10+5+(10/3) √6 = (15+ 10/3 ) √6 = (45/3 + 10/3 ) √6 = (55/3 ) √6
My God!
How to have such intuition!
brother...abc is ±√6000000
@@seekingCK OK. a+b+c = ±(55/3)√6
-(55√6)/3 or (55√6)/3
Yeah he missed the negative solution
i think so.
why negative
@@is7728why negative
(a+b+c)^2=6050/3
→a+b+c=+-√(6050/3)
___ ___
and in the case that all of a,b,c is negative ...
could you make
a+b+c=negative
How do you think about this ?
Excellent sollution
abc=100c
abc=200a => 11abc=600(a+b+c)
abc=300b
(abc)^2 = 100*200*300 => abc = +- √(100*200*300) = +- 1000*√6
a+b+c = 11abc/600 = +-11*1000*√6/600 = +-110/√6
Good idea
To simplify, let p=10a, q=10b and c=10c then
pq=1,qr=2, rp=3 and pqr^2=6
pqr=√6 or pqr=-√6
For pqr=√6
From pq=1 and pqr=√6, r = √6 since pq = 1
Also q = √6 / 2, p = √6 / 3
Finally a+b+c
= 10p+10q+10r
= 10 (p+q+r)
= 10 (√6/3+√6/2+√6)
= 10 (11√6 / 6
= 110√6 / 3
= 55√6 / 3
For pqr = -√6, a+b+c = -55√6/3
Sol: 55√6 / 3, -55√6 / 3
Very nice. I just recollected my mind for 70 years back momery
2a+2b+2c=600
Dived by 2
a+b+c =300
Right short answer
ab*bc*ca=(abc)^2=100*200*300. Then abc=1000*6^0.5. Then a=abc/bc=5*6^0.5
b=abc/ca=10/3*6^0.5
c=abc/ab=10*6^0.5
Then a+b+c=6^0.5(5+10/3+10)=55/3*6^0.5
a+b+c=250
Чувак не правильно решил: сократив корень и квадрат скобок, должен был получиться модуль, и на выходе два решения
ab+bc+ca=600. 2(a+b+c)=600. a+b+c=300
How 2a+2b+2c= ab+bc+ca ??????
how ab+bc+ca will become2(a+b+c) ????? New mathematical Theory...
Thanks sir 🎉
Your welcome. Thanks
a + b + c = 300
(a : 100 ; b: 0 dan c : 200 )
a=100, b=0, c=200
Спасибо. Я бы решила иначе, но ваш метод тоже интересен
Once you have values for a, b and c, you can simply add them.
Total a+ b + c =600
a
There is another short solution if we divide equation1 buy eq2
ab±bc±ca=600
2(a±b±c)= 600
a±b±చెప్పు =300
c=10sqrt6
b=10sqrt6/3
a=5sqrt6
ab.bc/ac=b^2=200/3
b=20/root 6
similarly
a=30/root 6
c=60/root 6
a+b+c=110/root6
this is shortest method
a=12.5,b=8,c=25
how is c/b 3:1? how do you kno this? can you explain please
Beautiful
Thank you! Cheers!
ab.bc.ca = a²b²c² = (abc)² = 100 . 200 . 300 = 6 . 10⁶
then abc = 6.10⁴, a.bc = 6.10⁴ , a.200= 6.10⁴ so a=3.10² , etc
awesome
Your welcome
There is a easiest way to solve this problem than that.
A100. B0. C200
சிறப்பு
Your welcome
a+b+c=45.5
is approximately 44.9073
Ab+bc+ca =100+200+300
2(a+b+c) = 600
A+b+c= 600/2
A+b+c = 300
350
What is final result?
you nedd not write every line ( a+B+C)*2put lhs an d rhs to denote left and right
You have left abc😮
10
Mistake ho chuki hae pl rechek caculation.
It's ok? You lose the same with minus
350
B=0
6
B= 0
600
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105
401
you are saying that a+b+c is equal to the numerator
D 200 E 900 F2
800
C=200
A=100
B=0
Simple
100
Прикольно, но всегда мучает вопрос - нафига это?
500
300
Есть ещё одно решение с минусом
👏👏
Your welcome
Цікаво 😊❤
Your welcome!
It's ok but what is useful in our regular life.
302
🤔
6oo/11 ans
Three hundred
Too lengthy
Okay but what is the numerical value ??? That’s what my question is
The numerical value could have been found about 1/3 of tge way in. YES, it would have been approximated, the precision would depend upon how many decimal places you choose to use.
@@robertloveless4938
No more than 2-3 decimal places would be fine for me.
,२००प्रतेकी
डोक्यावरुन गेले.
A- 100
B- 0
C- 200
A+B=100 100+0=100
B+C=200 0+200=200
C+A=300 200+100=300
A+B+C=? 100+0+200=300
A. 300
Hello why are you going this much critical. Easy & simple way A+B =100, (A is 100& B is 0). B&C=200(B is 0&C is 200), then. C+A=300(C is 200& A is 100).A+B+C= 300. 👌
Simple and super..
Then ab=0, pl read question carefully
సి స్క్వేర్ 600 లు యేమైంది
Very primitive methods
এত দীর্ঘ করে ভাল শিক্ষক অংক করে না। কথা শুদ্ধ করে পাঠদানে আশা উচিত।
またまた、虚数根つかうの😂辞めなよ
Modi ko bolo, woh bahut expert hai.
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