Question

Preciso muita dessa questão. Por favor,alguém pode me ajudar ?

Answer 1

Resposta:

15) 42                  16)  $\bold{2\sqrt{2}}$

Explicação passo-a-passo:

15)

$xy^2+x^2y\qquad\qquad x=3+\sqrt{2}\qquad y=3-\sqrt{2}\\\\\\ (3+\sqrt{2})(3-\sqrt{2})^2+(3+\sqrt{2})^2(3-\sqrt{2})= \\\\(3+\sqrt{2})(9-6\sqrt{2}+2)+(9+6\sqrt{2}+2)(3-\sqrt{2})=\\\\(3+\sqrt{2})(11-6\sqrt{2})+(11+6\sqrt{2})(3-\sqrt{2})=\\\\(33-18\sqrt{2}+11\sqrt{2}-6\sqrt{2}^2)\ +\ (33+18\sqrt{2}-11\sqrt{2}-6\sqrt{2}^2)=\\\\33-18\sqrt{2}+11\sqrt{2}-6.2\ +\ 33+18\sqrt{2}-11\sqrt{2}-6.2=\\\\66-18\sqrt{2}+11\sqrt{2}-12\ +\ 18\sqrt{2}-11\sqrt{2}-12=$

$66-12-12-18\sqrt{2}+11\sqrt{2}+18\sqrt{2}-11\sqrt{2}=\\\\ 66-24= \bold{42}$

16)

$(3+\sqrt{2}) - (3-\sqrt{2})=\\\\3+\sqrt{2}-3+\sqrt{2}=\\\\0+\sqrt{2}+\sqrt{2}=\bold{2\sqrt{2}}$