Hello My Dear Family😍😍😍 I hope you all are well 🤗🤗🤗 If you like this video about How to solve ³√(X + 28) - ³√(X - 28) = 2 please Like & Subscribe my channel as it helps me alot 🙏🙏🙏
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
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.
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.
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.
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 :)
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.
@@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.
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.
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...
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 🤣🤣😁
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.
