Question Number 135433 by naka3546 last updated on 13/Mar/21
$${Prove}\:\:{a}\:+\:\frac{\mathrm{1}}{{a}}\:\geqslant\:\mathrm{2}\:\:{for}\:\:{a}\:>\:\mathrm{0}\:\:{algebraically}\:. \\ $$
Answered by mr W last updated on 13/Mar/21
$${a}+\frac{\mathrm{1}}{{a}}=\left(\sqrt{{a}}−\frac{\mathrm{1}}{\:\sqrt{{a}}}\right)^{\mathrm{2}} +\mathrm{2}\geqslant\mathrm{2} \\ $$
Commented by naka3546 last updated on 13/Mar/21
$${Thank}\:{you},\:{sir}. \\ $$