Question

Se √a - √b = √2 e a - b = 6,então o valor de 1/(√a + √b ) é:

Answer 1

$a-b=( \sqrt{a}- \sqrt{b}).( \sqrt{a}+ \sqrt{b}) \quad logo\\6= \sqrt{2} .( \sqrt{a}+ \sqrt{b}) \\ \\( \sqrt{a}+ \sqrt{b})= \frac{6}{ \sqrt{2} }---\ \textgreater \ \frac{1}{( \sqrt{a}+ \sqrt{b})} = \frac{ \sqrt{2} }{6}$