Question

se x+y=8 e xy=15, qual e o valor de x²+6xy+y²?

a)109

b)120

c)124

d)154

Answer 1

x+y= 8
xy= 15
(x+y)^2=8^2
x^2+2xy+y^2= 64
x^2+y^2+2*15=64
x^2+y^2= 64-30
x^2+y^2= 34
34+ 6*15= 34+90= 124

Answer 2

                  x² + 6xy + y² -----------> x+y = 8  e  xy = 15
                  x² + y² + 6xy

                Sabendo que: x+y = 8                  
                                       (x+y)² = 8²
                                       x² + 2xy + y² = 64 ****substituindo xy = 15
                                       x² + 2.15 + y² = 64
                                       x² + 30 + y² = 64
                                       x² + y² = 64 - 30
                                       x² + y² = 34
       Logo:
                   x² + y² + 6xy =
                      34    + 6.15 =
                      34    + 90  = 124 <--- opção c