Simplificando a expressão 1 /√2+1 + 1/√2-1 obtemos:a) √2b) √2/2c) 2√2d) 2/3.... Pergunta de ideia dePepsi

May 2020 1 44 Report

Simplificando a expressão 1 /√2+1 + 1/√2-1 obtemos:

a) √2
b) √2/2
c) 2√2
d) 2/3

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Eriivan

Verified answer

$\frac{1}{( \sqrt{2}+1 )} + \frac{1}{( \sqrt{2}-1 )}$

Multiplicando cada parcela pelo conjugado

$\frac{1}{( \sqrt{2}+1 )}. \frac{(\sqrt2-1)}{(\sqrt2-1)} + \frac{1}{( \sqrt{2}-1 )} . \frac{(\sqrt2+1)}{(\sqrt2+1)}$

$\frac{ \sqrt{2} -1}{2-1} + \frac{\sqrt2+1}{2-1}$

$\sqrt{2} -1+ \sqrt{2}+1$

$\boxed{\boxed{2 \sqrt{2} }}$

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