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

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- Jan 27th 2011, 06:24 AMjacksCalculate 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 AMProve It
In short, no solutions exist...

- Jan 27th 2011, 06:40 AMjacks
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 AMKrizalid
zero is a solution, i just checked it by eye.

- Jan 27th 2011, 10:40 AMKrahl
http://img35.imageshack.us/img35/6717/rootsl.jpg

plot using maple.

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

http://img148.imageshack.us/img148/2136/roots2.jpg - Jan 27th 2011, 05:41 PMProve It
- Jan 27th 2011, 07:36 PMKrizalid
i think you can now understand me why i'm telling that you don't have to absolutely trust on wolfram everytime.