Question

(UFRGS) O quociente entre 3 + 2√2 e √2 + 1 é:
a) 2 + 1.
b) 2 − 1.
c) 5 2 + 7.
d) 5/2.
e) 3
2
+ 2 2.

Answer 1

Explicação passo-a-passo:

$\sf \dfrac{3+2\sqrt{2}}{\sqrt{2}+1}$

$\sf =\dfrac{3+2\sqrt{2}}{\sqrt{2}+1}\cdot\dfrac{\sqrt{2}-1}{\sqrt{2}-1}$

$\sf =\dfrac{3\sqrt{2}+2\cdot2-3-2\sqrt{2}}{(\sqrt{2})^2-1^2}$

$\sf =\dfrac{3\sqrt{2}+4-3-2\sqrt{2}}{2-1}$

$\sf =\dfrac{\sqrt{2}+1}{1}$

$\sf =\red{\sqrt{2}+1}$

Letra A