Question

Solve ${\log }_{\frac{1}{2}}{n}^2+1\ge 0$

Answer 1

${\log }_{\frac{1}{2}}(n{)}^2+1\ge 0$

$⟹{\log }_{\frac{1}{2}}(n{)}^2\ge -1$

$⟹n^2\ge (\frac{1}{2}{)}^{-1}=2$

$⟹n^2-2\ge 0$

$⟹(n+\sqrt{2})(n-\sqrt{2})\ge 0$

$\therefore nϵ[-\infty ,-\sqrt{2})\cup (\sqrt{2},\infty ]$