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

$(x + y) = {x}^{2} + 2xy + {y}^{2} = {13}^{2} = 169$

Se xy = 1 temos:

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