# Thread: Abstract, find the solution from an equation

1. ## Abstract, find the solution from an equation

Find the solution that is given by the equation

x = cubedroot((-q/2)+sqrt(((q^2)/(4))+((p^3)/(27))) - cubedroot((q/2)+sqrt(((q^2)/(4))+((p^3)/(27)))

Just need a little help here, I think I solved it by cubing everything and getting x^3 = -q so my answer is (x^3 + q) = 0. Does that look right?

Then I need to show that the solution above really is 2 with a hint of find (sqrt(3) + 1)^3 and (sqdrt(3)-1)^3 which I only somewhat see how it is related.

Anyone who can verify my first part and maybe give me a little guidance on the second part?

Thanks a lot

As for the second part, I have an idea, but I think it's wrong. Since x = 2, q must equal 8 so then do I just solve for p and show it holds? I don't know if that actually proves anything and doesn't use the hint.

edit: I'm pretty sure the solution is 2 means q is 2

2. ## Re: Abstract, find the solution from an equation

Originally Posted by Johngalt13
Find the solution that is given by the equation

x = cubedroot((-q/2)+sqrt(((q^2)/(4))+((p^3)/(27))) - cubedroot((q/2)+sqrt(((q^2)/(4))+((p^3)/(27)))
$x =$

Just need a little help here, I think I solved it by cubing everything and getting x^3 = -q so my answer is (x^3 + q) = 0. Does that look right?
wrong you cant distribute the power at the addition of subtraction it distribute at the multiplication and division
$(a+b)^3 \ne a^3 + b^3$

in general

$(a - b )^3 = a^3 - 3 a^2b + 3 ab^2 - b^3$

use it to expand

$\left(\sqrt[3]{\frac{-q}{2} + \sqrt{\frac{q^2}{4}+\frac{p^3}{27}}} - \sqrt[3]{\frac{q}{2}+ \sqrt{\frac{q^2}{4} + \frac{p^3}{27}}}\right)^3$