# Calculate value of x

• Jan 27th 2011, 06:24 AM
jacks
Calculate value of x
Calculate value of $\displaystyle x$ in $\displaystyle (7x+1)^{\frac{1}{3}}+(-x^2+x+8)^{\frac{1}{3}}+(x^2-8x-1)^{\frac{1}{3}}=2$
• Jan 27th 2011, 06:32 AM
Prove It
In short, no solutions exist...
• Jan 27th 2011, 06:40 AM
jacks
How can I say.....

Here is my process...

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

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

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

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

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

Now I am struck at that point.......
• Jan 27th 2011, 08:33 AM
Krizalid
zero is a solution, i just checked it by eye.
• Jan 27th 2011, 10:40 AM
Krahl
• Jan 27th 2011, 05:41 PM
Prove It
Quote:

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...
• Jan 27th 2011, 07:36 PM
Krizalid
i think you can now understand me why i'm telling that you don't have to absolutely trust on wolfram everytime.