Question

(obmep-mep) se x+y=8 e xy=15, qual é o valor de x^2+6xy+y^2?

Answer 1

${x}^{2} + 6xy + {y}^{2} = {x}^{2} + 2xy + 4xy + {y}^{2} = \\ = {x}^{2} + 2xy + {y}^{2} + 4xy = \\ = {(x + y)}^{2} + 4xy = \\ = {8}^{2} + 4 \times 15 = \\ = 64 + 60 = 124$