已知x+y=-10,xy=16

问题描述:

已知x+y=-10,xy=16
①x^2+y^2 ②(x-y)^2 ③(x+2)(y+2) ④x^2-xy+y^2

x^2+y^2=x^2+y^2+2xy-2xy=(x+y)^2-2xy=(-10)^2-2*16=100-32=68
(x-y)^2=x^2+y^2-2xy=68-2*16=36
(x+2)(y+2)=xy+2x+2y+4=16-20+4=0
x^2-xy+y^2=x^2+y^2-xy=68-16=52