Question

1-Calcule o resultado das expressões abaixo:
a)$10 \sqrt{2} * ( \sqrt{2} + \sqrt{2} * \sqrt{2} - 2 )$

b)    $\frac{1}{2+ \sqrt{3} } + \frac{1}{2- \sqrt{3} }$

Answer 1

$a)\ 10\sqrt{2} \times ( \sqrt{2} + \sqrt{2} \times \sqrt{2} - 2 )\\\\ =10\sqrt{2} \times ( \sqrt{2} + \sqrt{2 \times 2} - 2 )\\ =10\sqrt{2} \times ( \sqrt{2} + \sqrt{4} - 2 )\\ =10\sqrt{2} \times ( \sqrt{2} + 2 - 2 )\\ =10\sqrt{2} \times \sqrt{2}\\ =10\sqrt{2 \times 2}\\ =10\sqrt{4}\\ =10 \times 2\\ \boxed{=20}$

$b)\ \dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\\\\\\ =\dfrac{2-\sqrt{3} + 2 + \sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}\\\\\\ =\dfrac{4}{4-2\sqrt{3}+2\sqrt{3}+\not\sqrt{3}^{\not2}}\\\\\\ =\dfrac{4}{4-3}\\\\\\ =\dfrac{4}{1}\\\\\\ \boxed{=4}$

Bons estudos!