Question

Seja o número real k, tal que k=1/(√2+√3)+1/(√2-√3) . Sobre o valor de k é correto afirmar que:
a) k ∈ Z tal que k > 0.
b) k ∈ LR tal que k < – 2.
c) k ∈ Q tal que k < 2.
d) k ∈ I tal que k > 2.

Answer 1

$\boxed{\begin{array}{l}\sf k=\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{2}-\sqrt{3}}\\\sf k=\dfrac{\sqrt{2}-\diagup\!\!\!\!\!\sqrt{3}+\sqrt{2}+\diagup\!\!\!\!\!\sqrt{3}}{(\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3})}\\\sf k=\dfrac{2\sqrt{2}}{(\sqrt{2})^2-(\sqrt{3})^2}\\\sf k=\dfrac{2\sqrt{2}}{2-3}\\\sf k=\dfrac{2\sqrt{2}}{-1}\\\sf k=-2\sqrt{2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}}\end{array}}$