Question

Mostre que o inverso de √2-1 é √2+1

Answer 1

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