<s>[INST] $x(x^2-2)=0$, The answers are $x = 0, \sqrt{2}$, how do I get there? $$x(x^2-2)=0$$
The answers are $x=\sqrt{2}, 0$ how do I get there?
 [/INST] First recall some elementary algebra that if $A\cdot B = 0$, then $A = 0$ or $B = 0$ or both of them $A = 0, B = 0$. So $x(x^2-2) = 0 \to x = 0$ or $x^2-2 = 0$, and $x^2-2 = 0 \to (x-\sqrt{2})(x+\sqrt{2}) = 0 \to x-\sqrt{2} = 0$ or $x +\sqrt{2} = 0 \to x = \sqrt{2}$ or $x = -\sqrt{2}$. Thus there are $3$ solutions: $x = 0,-\sqrt{2}, \sqrt{2}$.
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