Question

Se x+y= 13 e x.y=1 então x² + y² é

A)166
B)167
C)168
D)169
E)170

Answer 1

Olá Jéssica!

$\\ \mathsf{x + y = 13} \\\\ \mathsf{(x + y)^2 = (13)^2} \\\\ \mathsf{x^2 + 2xy + y^2 = 169} \\\\ \mathsf{x^2 + y^2 + 2 \cdot xy = 169} \\\\ \mathsf{x^2 + y^2 + 2 \cdot 1 = 169} \\\\ \mathsf{x^2 + y^2 = 169 - 2} \\\\ \boxed{\mathsf{x^2 + y^2 = 167}}$