Question

efetue : 1/1+raiz de 7 + 1/1-raiz 7 o resultado sera :

resultado da -1/8

Preciso do cálculo
Me ajudem pff

Answer 1

$\dfrac{1}{1+ \sqrt{7}} + \dfrac{1}{1- \sqrt{7} } = \\ \\ \\ \star \dfrac{1}{1+ \sqrt{7}}*\dfrac{1- \sqrt{7} }{1- \sqrt{7}}= \dfrac{1- \sqrt{7} }{(1)^2-( \sqrt{7})^2}= \dfrac{1- \sqrt{7} }{1-7}= \dfrac{1- \sqrt{7} }{-6}= \dfrac{-1+ \sqrt{7} }{6}\\ \\ \\ \star \dfrac{1}{1- \sqrt{7}}*\dfrac{1+ \sqrt{7} }{1+ \sqrt{7}}= \dfrac{1+ \sqrt{7} }{(1)^2-( \sqrt{7})^2}= \dfrac{1+ \sqrt{7} }{1-7}= \dfrac{1+ \sqrt{7} }{-6}= \dfrac{-1- \sqrt{7} }{6}$

$\dfrac{-1+ \sqrt{7} }{6}+ \dfrac{-1- \sqrt{7} }{6}= \dfrac{-1-1}{6}= \dfrac{-2}{6}= \boxed{ \dfrac{-1}{3}}$