# Number in Q

• June 7th 2009, 06:48 AM
dhiab
Number in Q
• June 7th 2009, 08:27 AM
running-gag
Quote:

Originally Posted by dhiab

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 $\sqrt[3]{3+\sqrt{9+\frac{125}{27}}}-\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}} = 1$