Question

A expressão (√3 - √5)² + (√3 + √5)² + (√3 - √5).(√3 +√5) é equivalente a:
a) 14 + √15
b)14-4√15
c)14
d)0
e)19

Answer 1

$(\sqrt{3})^{2}-2\sqrt{3}\sqrt{5}+(\sqrt{5})^{2}+(\sqrt{3})^{2}+2\sqrt{3}\sqrt{5}+(\sqrt{5})^{2}+(\sqrt{3})^{2}-(\sqrt{5})^{2}=$
$3-2\sqrt{15}+5+3+2\sqrt{15}+5+3-2=$
$14$

Answer 2

Resposta:

Alternativa C

Explicação passo-a-passo:

1) (√3 - √5)² + (√3 + √5)² = 3 + - $2\sqrt{15}$ + 5 + 3 + $2\sqrt{15}$ + 5 = 16

(√3 - √5)² = $\sqrt{9$ - $2\sqrt{15}$ + $\sqrt{25}$

(√3 + √5)² = $\sqrt{9$ + $2\sqrt{15}$ + $\sqrt{25}$

 

2) (√3 - √5).(√3 +√5) = $\sqrt{9$ + $\sqrt{15\\}$ -  $\sqrt{15\\}$ - $\sqrt{25}$ = 3 - 5 = -2

3) 16 - 2 = 14 - Alternativa C