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Prove-a-1-a-2-for-a-gt-0-algebraically-




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

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