+9675 My cousin is challenging me in Mathematics. He gave me this question and I still can't solve it for 1 week.
He said that the solution is x = 8, I plugged x = 8 into the equation and it is correct. But I don't know how to get the answer. He told me the question and the answer and he told me to do the steps.
If x = 8, then substitute it into the equation and see what you get. This is what will get!
8^1/3 +(8 - 16)^1/3 =(8 - 8)^1/3
2 + (-8)^1/3 = 0^1/3
2 + 2(-1)^1/3=0 ????????
+259 x1/3+(x−16)1/3=(x−8)1/3
Now take every side ^3
x + x - 16 = x - 8. I+16. I -x
x = 8
+259 Cant I take every side ^3? I know the answer looked really simple but who knows ^^
+356 (x)^1/3 + (x - 16)^1/3 = (x - 8)^1/3------------Cube each side
3 (x - 16)^(1/3) x^(2/3) + 2 x + 3 (x - 16)^(2/3) x^(1/3) - 16 = x - 8 -------------Isolate all radicals
3 (x - 16)^(1/3) x^(2/3) + 3 (x - 16)^(2/3) x^(1/3) = -x + 8
idk what to do from here LOL. Thats what we learned in school with square roots. But that is Algebra 2 and this is NOT algebra 2! I am about to go to school and gonna see if my teacher can do it and get back to you.
+118703 You know Ninja, you are a smart kid - yes I know you already know that LOL
I think you should start to learn some Latex. It is easy, you can learn it a little at a time and think how smart you will look then! :))
Take this line
(x)^1/3 + (x - 16)^1/3 = (x - 8)^1/3
It is not to the power of 1 it is to the power of 1/3 so put the 1/3 s in parentheses. Like this
(x)^{1/3} + (x - 16)^{1/3} = (x - 8)^{1/3}
Now copy that line onto your clipbard
now open the latex tab and copy it in.
like this
(x)1/3+(x−16)1/3=(x−8)1/3
Now if you copy what I have done you will have used LaTex for the first time :))
If you have questions make sure you ask.
We have had at least one boy on here before, I think he was a lot younger than you, and he got really good at LaTex.
+118703 Yes I could not do any LaTex until I was on this forum. I didn't learn the basics here because back then this forum did not have Latex. Mr Massow added it for us quite a bit later :)
But smart kids like you and Max and MathsGod can learn it really quickly if you put your mind to it. :)
+118703 I was looking at this expansion in Wolfram Alpha
expansion of (-a+x)^(1/3)
and the expansion is
There is an obvious pattern here except why are both the first two terms + and then the signs alternate.
Why is that ?
Perhaps I should have put this as a new question but it is sideways related to this question ://
+9675 To make the sign alternate:
3√−a=−3√a
At least this is true according to my knowledge.
+9675 Finally I have the answer!!!
x1/3+(x−16)1/3=(x−8)1/3x+x−16+3x1/3(x−16)2/3+3x2/3(x−16)1/3=x−83x1/3(x−16)1/3((x−16)1/3+x1/3)=8−x(x1/3(x−16)1/3(x−8)1/3)=8−x3x3−24x2−128x=(x−8)3−27x3−24x2−128x=−x3+24x2−64x+5122728x3−672x2+(128×28−192)x−512=028x3−672x2+3648x−512=0(x−8)(7x2−112x+16)=0x=8 or 8+12√37 or 8−12√37
