<s>[INST] Inequality with condition $x^2+y^2+z^2=1$. let $x,y,z>0$ such that $x^2+y^2+z^2=1$. Find the minimum of $$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$$
Is the answer $3\sqrt{3}$ by any chance?
 [/INST] Apply AM-GM and CS inequalities:$$\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z} \geq \dfrac{9}{x+y+z} \geq \dfrac{9}{\sqrt{3}\cdot (x^2+y^2+z^2)}= 3\sqrt{3}$$
</s>