It can be done much more simple. From a -b = 2 it is a = b + 2. Take both sides to the third power and you get: a^3 = b^3 + 6b^2 +12b +8. You know a^3 - b^3 = 56, so you get a simple quadratic equation in b, with solutions -4 and 2. This will get the two solutions for x.
I speak a little english but the maths is a language unviversal, I can be wrong but why did the man write a^3-b^3=x+28-x+28 instead mustn't he write a^3-b^3=x+28-x-28
Super super long way, but it shows a logical process of substitution used in harder problems. I just saw the answer by observation in a few seconds because the problem is so common, and basic. Yhere are other ways to solve these.
That's real fast! And how long would it take you when you change 2 in the original equation in let's say 12? The fun of mathematics is not the solution but the way to get it
I think I found better solution: Consider x + 28 = y^3 x - 28 = y^3 - 56 Now we have (y-2)^3 = y^3 - 56 simplifying we attain this quadratic y^2 -2y - 8 = 0 Clearly, we have y = 4 or -2. From there its pretty easy to see that 36 or -36 is the answer. Didn't read all the comments, if someone else came up with it first take the credit :)
Observando as raízes cúbicas, os números inteiros positivos cuja a diferença de suas raízes cúbicas é 2 são: 27 e 1, 64 e 8, 125 e 27, 216 e 64, etc. E assim por diante... Após testar por substituição, o único par em que o valor de x dentro da raiz cúbico tem o mesmo valor (x = 36) é o par 64 e 8. Portanto, a única solução inteira positiva é x = 36. Na verdade não precisa de tanta álgebra assim.
Hola: usted se complica demasiado. Termina mucho antes haciendo x-28=a^3. De esta manera, x+28=a^3+56. Así, se obtiene que la raíz cúbica de a^3+56 es igual a 2+a y al elevar al cubo ambos miembros de la igualdad, la ecuación se reduce a a^2+2a-8=0, cuyas soluciones son a=-4 y a=2. Del primer caso resulta x=-36 y del segundo, x=36. Hay dos soluciones. Un saludo.
There is an idiom that sais you turned the food around your head to put it in your mouth , you could solve it by half of the paper , but at the sane time it was a logical way , any way thank you i enjoyed 👍🏻🙏🏻❤️
x must be greater than 28 and the two cubic roots must return an integer. Without algebraic calculation the only real solution is 36 ... just checked your video. I didn't consider the negative values so as you stated, also -36 is a solution.
Sure, here is the answer to the question "x=?" in English: Given the equation: ``` \sqrt[3]{x+28}-\sqrt[3]{x-28}=2 ``` Multiplying both sides by $(x+28)^{2/3}(x-28)^{2/3}$, we get: ``` (x+28)^{2/3}-(x-28)^{2/3}=2(x+28)^{1/3}(x-28)^{1/3} ``` Squaring both sides, we get: ``` (x+28)^{4/3}-2(x+28)^{2/3}(x-28)^{2/3}+(x-28)^{4/3}=4(x+28)^{1/3}(x-28)^{1/3} ``` Simplifying, we get: ``` x^2-564=2x^2-48 ``` Solving for x, we get: ``` x=\boxed{36} ``` Here is a step-by-step solution: 1. Multiply both sides by $(x+28)^{2/3}(x-28)^{2/3}$. ``` (x+28)^{2/3}-(x-28)^{2/3}=2(x+28)^{1/3}(x-28)^{1/3} ``` 2. Square both sides. ``` (x+28)^{4/3}-2(x+28)^{2/3}(x-28)^{2/3}+(x-28)^{4/3}=4(x+28)^{1/3}(x-28)^{1/3} ``` 3. Simplify. ``` x^2-564=2x^2-48 ``` 4. Solve for x. ``` x=\boxed{36} ``` **Notes:** * In the solution process, it is important to check that the dimensions on both sides of the equation are consistent. * When solving the equation, it is important to check that the root of the equation satisfies the given condition of the problem.
@@woobjun2582 as long as the number inside the sqrt is positive then yes, you will have both a positive and a negative number as an answer because if you square the negative -1.1414 you will get back your positive 2.
@@charlesmitchell5841 I know, when you want to find answer for the x^2 = 2 then your comment is yes, such that it's +1.414 and -1.414. BUT on your process of solving, sqrt(36) is only +6 !!!
@@charlesmitchell5841 After all.(1) If try to solve x^2 = 36, then x is +6 or -6. (2) If try to solve x = sqrt(36), then x = +6 only. This is what I am talking. Plz consulted the definition of square roots.
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Really unnecessary substitutions, a and b both are function of x. Goal is to solve x. Could just cube the original equation and go from there, I finished before 1/3 of the video.
Sorry but there is a mistake: you cannot consider X = -36, because the cubic root is only applicable on positive numbers, in this case you would have a cubic root of -36-28=-64. Only the value X=36 is possible except if you are in a complex space, in this case the cubic root of ‘-64’ would give 4i.
Actually you got the wrong idea sir; the odd roots carry negative values whereas even roots are inadmissible to negative values. So even roots: positive numbers only odd roots: positive and negative numbers. Example: -2 × -2 × -2 = -8, that is proof that it holds negative numbers... Cube root of -8 is -2...
Here is simple solution. Find the first number which makes (x +28)^(1/3) perfect cube I.e 36 . It satisfies the given equation.lExploring simple solution could save lots of time.
Once you get ab=8 you can simply substitute back with the cubic roots and get (x+28)(x-28)=8³
Yes I think so, too.
You forgot the - between
After this lady explanation, math looks verry eassy!🎉
a-b=2 and ab=8 => b=8/a plug the value of b in first so that it will become a quadratic equation.
It can be done much more simple. From a -b = 2 it is a = b + 2. Take both sides to the third power and you get: a^3 = b^3 + 6b^2 +12b +8. You know a^3 - b^3 = 56, so you get a simple quadratic equation in b, with solutions -4 and 2. This will get the two solutions for x.
I speak a little english but the maths is a language unviversal, I can be wrong but why did the man write a^3-b^3=x+28-x+28 instead mustn't he write a^3-b^3=x+28-x-28
consider x-28 in paranthesis. Directly multiplied minus sign. - (X-28) = -X+28@@octaviopietronave8575
@@octaviopietronave8575 a^3 - b^3 = (x+28) - (x-28) = x+28 - x + 28
13:53 although very complicated but also very educative and interesting
Thank you very much
Of coluse
Super super long way, but it shows a logical process of substitution used in harder problems. I just saw the answer by observation in a few seconds because the problem is so common, and basic. Yhere are other ways to solve these.
Power 3 both sides and use formula (a-b)^3= a^3 -3a^2b+3ab^2 -b^3 = 8 continue solution until you get x^2-28^2 = 8^3
So x^2 = 1296 then x=+36 or x=-36
you are one of the best teacher's out there keep it up !!!!
Thank you! 🙏❤️🙏
I just look at candidate integer cubes and quickly 64 and 8 pop out. So X =36 yields 36+28 = 64 and 36-28 = 8.
64^(1/3) - 8^(1/3) = 4 - 2 = 2
I got the answer by a different and easy way
Show us please
I used log function and solved much easier.
Guys i am not a math pro but an engineer. And i saw that x is 36, when i looked it in 4-5 seconds
That's real fast! And how long would it take you when you change 2 in the original equation in let's say 12? The fun of mathematics is not the solution but the way to get it
I think I found better solution:
Consider
x + 28 = y^3
x - 28 = y^3 - 56
Now we have
(y-2)^3 = y^3 - 56
simplifying we attain this quadratic
y^2 -2y - 8 = 0
Clearly, we have y = 4 or -2.
From there its pretty easy to see that 36 or -36 is the answer.
Didn't read all the comments, if someone else came up with it first take the credit :)
Observando as raízes cúbicas, os números inteiros positivos cuja a diferença de suas raízes cúbicas é 2 são: 27 e 1, 64 e 8, 125 e 27, 216 e 64, etc. E assim por diante... Após testar por substituição, o único par em que o valor de x dentro da raiz cúbico tem o mesmo valor (x = 36) é o par 64 e 8. Portanto, a única solução inteira positiva é x = 36. Na verdade não precisa de tanta álgebra assim.
Hola: usted se complica demasiado. Termina mucho antes haciendo x-28=a^3. De esta manera, x+28=a^3+56. Así, se obtiene que la raíz cúbica de a^3+56 es igual a 2+a y al elevar al cubo ambos miembros de la igualdad, la ecuación se reduce a a^2+2a-8=0, cuyas soluciones son a=-4 y a=2. Del primer caso resulta x=-36 y del segundo, x=36. Hay dos soluciones. Un saludo.
Африканец, ты молодец, так держать.
Thay a=2+b (1) vào (4) rồi tính tiếp là được mà.
Put: t=3√(x+28)
t3= x+28
t3-28 =x
become t - 3√(t-28-28) =2
(t-2)3 = (3√t-56)3
=>6t2 - 12t - 48=0
=> t = 4 , x = 36; t= -2 , x= -36
(t-2)^3=t-56, how get then that square equation?
Nice
super👋👏👍👍👍
Thank you 👍👍👍
🌹🌹🌹🌹🌹
❤️❤️❤️
Very clever solution!
Thanks for your teach.
You are welcome!🙏❤️🙏
Wwooww😮
This is very simple task
There is an idiom that sais you turned the food around your head to put it in your mouth , you could solve it by half of the paper , but at the sane time it was a logical way , any way thank you i enjoyed 👍🏻🙏🏻❤️
Thank you 👍👍
Bro's handwriting is immaculate
Yeah, but he can't spell
You can write original question as
X^3 - (x-2)^3 = 98
Expand and solve
Sorry not 98, but 56
ab =8, a-b = 2, a, b can be solved already
36 😂 the answer could be from the 2^3 or 4^3 or any (2^x)^3 so I just tried 4 and it works!
You didn’t need equation 3 at all. Once you derived ab=8, you can use the fact that a-b=2 to solve this: a=4, b=2 (or a=-2, b=-4).
It can be much simpler!
Unnecessary calculations..put a=b+2 in a3-b3 and done!
Very long. We may paste (1) to (3) and resolve quadratic equation
By eqs (1)&(4), a(a-2)=8
So a=4 or -2 and get
x=36, -36. You can save 8 minutes.
There is another sampler method. Take whole cube of both side first. Then go on
much simpler
What do you mean " box " ??? I dont see any box..
OMG
Desmos = +\- 36 👍
x must be greater than 28 and the two cubic roots must return an integer. Without algebraic calculation the only real solution is 36 ... just checked your video. I didn't consider the negative values so as you stated, also -36 is a solution.
Sure, here is the answer to the question "x=?" in English:
Given the equation:
```
\sqrt[3]{x+28}-\sqrt[3]{x-28}=2
```
Multiplying both sides by $(x+28)^{2/3}(x-28)^{2/3}$, we get:
```
(x+28)^{2/3}-(x-28)^{2/3}=2(x+28)^{1/3}(x-28)^{1/3}
```
Squaring both sides, we get:
```
(x+28)^{4/3}-2(x+28)^{2/3}(x-28)^{2/3}+(x-28)^{4/3}=4(x+28)^{1/3}(x-28)^{1/3}
```
Simplifying, we get:
```
x^2-564=2x^2-48
```
Solving for x, we get:
```
x=\boxed{36}
```
Here is a step-by-step solution:
1. Multiply both sides by $(x+28)^{2/3}(x-28)^{2/3}$.
```
(x+28)^{2/3}-(x-28)^{2/3}=2(x+28)^{1/3}(x-28)^{1/3}
```
2. Square both sides.
```
(x+28)^{4/3}-2(x+28)^{2/3}(x-28)^{2/3}+(x-28)^{4/3}=4(x+28)^{1/3}(x-28)^{1/3}
```
3. Simplify.
```
x^2-564=2x^2-48
```
4. Solve for x.
```
x=\boxed{36}
```
**Notes:**
* In the solution process, it is important to check that the dimensions on both sides of the equation are consistent.
* When solving the equation, it is important to check that the root of the equation satisfies the given condition of the problem.
I was wondering if you could take the derivative on both sides, I dunno if it works but it should
X = {36,-36}
You can simply sub equation 1 into 2 to get a simple quadratic equation. Why make things so complicated
Time swallow all steps.. Just 4 steps along with logic possibilities enough..
You only needed the first 2 equations to solve it.
اش ايدك استاد
sqrt(36) is NOT +6 & -6, it is just +6. But in case, x^2 = 36 then you can say x = +6 & -6. Plz think of it.
Why is it just +6 when if you square both +6 and-6 you get 36 ?
@@charlesmitchell5841 then, what is the answer for sqrt(2)? Is that +1.414 and -1.414? NOPE it's just +1.414 as far as I know
@@woobjun2582 as long as the number inside the sqrt is positive then yes, you will have both a positive and a negative number as an answer because if you square the negative -1.1414 you will get back your positive 2.
@@charlesmitchell5841 I know, when you want to find answer for the x^2 = 2 then your comment is yes, such that it's +1.414 and -1.414. BUT on your process of solving, sqrt(36) is only +6 !!!
@@charlesmitchell5841 After all.(1) If try to solve x^2 = 36, then x is +6 or -6. (2) If try to solve x = sqrt(36), then x = +6 only. This is what I am talking. Plz consulted the definition of square roots.
With respect, but way easier method to solve it is available
-36;36
36
You missed checking it
(1+1/x)^x=3
Knp 2 dlm satu hr ada 2 siang ada malam..ada gelap ada tetang hrsnya 3..yg satunya cahaya brother..itu masuknya ke 7 hri ada siang malam mjd 28 haha brother...🤣😁
Itu teori asam basa...mana cahayanya Cnya 🤣🤣😁
Olimpíada fácil
Х=36
This is such a long process.
Trick - Top 2 global Geometry Dash player. You should know this Trick.
Really unnecessary substitutions, a and b both are function of x. Goal is to solve x.
Could just cube the original equation and go from there, I finished before 1/3 of the video.
That is easy. In Turkey, this kind of question is for High college entrance exams.
Наугад ровно 36
X=36
84-28=56 not 36
I wonder this took almost 14 mins and steps to be solved😂😂
Attention a+b>0
Misalı uzun yolla yazmısan.kuba yükseltsen asanlıqla alınar
This is the most bizarre thing I've ever seen on RUclips.
"Focus" is not spelled as "Focuss"!
If u solve this slo …
aとbを置き換えた時点でa>0、b>0と置き換えないとダメですね。x=-36では複素数になっちゃいます。
Решить можно еще легче! Замутили лишнее!
Sorry but there is a mistake: you cannot consider X = -36, because the cubic root is only applicable on positive numbers, in this case you would have a cubic root of -36-28=-64. Only the value X=36 is possible except if you are in a complex space, in this case the cubic root of ‘-64’ would give 4i.
Actually you got the wrong idea sir; the odd roots carry negative values whereas even roots are inadmissible to negative values.
So even roots: positive numbers only
odd roots: positive and negative numbers.
Example: -2 × -2 × -2 = -8, that is proof that it holds negative numbers...
Cube root of -8 is -2...
36; -36. Других корней нет. Использованы свойства монотонных функций.
Да, только решение громадное
в любом случае раза в три короче, чем у автора.
А разве подкоренное выражение может быть отрицательным? 😮
@@user-dfhhbfhghfgdf
Может. Ведь это не квадратный корень)
Why do you keep saying mayonnaise?
Sounds like Indian.立方差公式直接秒解。
Worst way to solve the problem
No sir.i think it is also an easy method
it’s too long method !
Solution is only 36 because under root cant be less than 0.
Oh no. Power is 1/3. My bad
Too complicated. I can be easer than that
a and b cannot be negative so 2nd case is impossible
Here is simple solution. Find the first number which makes (x +28)^(1/3) perfect cube I.e 36 . It satisfies the given equation.lExploring simple solution could save lots of time.
Too slow
This guy writes arithmetic processes too much.
Very non-effective way to solve mathematics.
36
X=36
Too slow
36
X=36