# Math Help - Calculate value of x

1. ## Calculate value of x

Calculate value of $x$ in $(7x+1)^{\frac{1}{3}}+(-x^2+x+8)^{\frac{1}{3}}+(x^2-8x-1)^{\frac{1}{3}}=2$

2. In short, no solutions exist...

3. How can I say.....

Here is my process...

Let $(7x+1)^{\frac{1}{3}}=a$

$(-x^2+x+8)^{\frac{1}{3}}=b$

$(x^2-8x-1)^{\frac{1}{3}}=c$

So We Get $a+b+c=a^3+b^3+c^3$

$a(a^2-1)+b(b^2-1)+c(c^2-1)=0$

Now I am struck at that point.......

4. zero is a solution, i just checked it by eye.

5. plot using maple.

x=-1,x=0,x=1 and x=9

6. Originally Posted by Krizalid
zero is a solution, i just checked it by eye.
Interesting, Wolfram said "No Solutions Exist..."

But you're right, 0 works...

7. i think you can now understand me why i'm telling that you don't have to absolutely trust on wolfram everytime.