Calculate value of x

**jacks** · January 27th 2011, 06:24 AM

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

**Prove It** · January 27th 2011, 06:32 AM

In short, no solutions exist...

**jacks** · January 27th 2011, 06:40 AM

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.......

**Krizalid** · January 27th 2011, 08:33 AM

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

**Krahl** · January 27th 2011, 10:40 AM

plot using maple.

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

**Prove It** · January 27th 2011, 05:41 PM

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...

**Krizalid** · January 27th 2011, 07:36 PM

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

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