Question

Se x^2 + 1/x^2 = 2, o valor de x + 1/x é:

a) 1
b) 2
c) 3
d) 4
e) 5

Answer 1

Explicação passo-a-passo:

$\sf \left(x+\dfrac{1}{x}\right)^2=x^2+2\cdot x\cdot\dfrac{1}{x}+\dfrac{1}{x^2}$

$\sf \left(x+\dfrac{1}{x}\right)^2=x^2+2+\dfrac{1}{x^2}$

$\sf \left(x+\dfrac{1}{x}\right)^2=x^2+\dfrac{1}{x^2}+2$

$\sf \left(x+\dfrac{1}{x}\right)^2=2+2$

$\sf \left(x+\dfrac{1}{x}\right)^2=4$

$\sf x+\dfrac{1}{x}=\sqrt{4}$

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

Letra B