Question

Qual o valor da expressão √2/√2+1 é:

Answer 1

Resposta:

$\dfrac{ \sqrt{2} }{ \sqrt{2} + 1} \times \dfrac{ \sqrt{2} - 1 }{ \sqrt{2} - 1 } = \\ \\ = \dfrac{ \sqrt{2}( \sqrt{2} - 1) }{( \sqrt{2} + 1)( \sqrt{2} - 1)} \\ \\ = \dfrac{ \sqrt{2 \times 2} - \sqrt{2} }{ { ( \red\not\sqrt{2}) }^{ \red \not2} - {(1)}^{ 2} } \\ \\ = \dfrac{ \sqrt{4} - \sqrt{2} }{2 - 1} \\ \\ = \dfrac{2 - \sqrt{2} }{1} \\ \\ = \LARGE\boxed{ \bf \green{2 - \sqrt{2} }} \\ \\ \boxed{\LARGE \bf \blue{ \underline{Bons \: Estudos}!}}$