# Math Help - Number in Q

1. ## Number in Q

prouve :

2. Originally Posted by dhiab
prouve :

Hi

If you consider the equation $x^3+5x-6=0$ you can find that x=1 is the only real solution since $x^3+5x-6=(x-1)(x^2+x+6)$

Now if you try to solve it using Cardan method Méthode de Cardan - Wikipédia you will find that one real solution is

$\sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}}$

Since 1 is the only real solution you get $\sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}} = 1$