已知x+xy=14,y²+xy=2,求(1)(x+y)²-x²+y²（2）x+y

Question

已知x+xy=14,y²+xy=2,求(1)(x+y)²-x²+y² （2）x+y

Answer 1

已知x ² +xy=14,y²+xy=2,求(1)(x+y)²-x²+y² （2）x+y

(1)(x+y)²-x²+y²
=x²+2xy+y²-x²+y²
=2xy+2y²
=2(xy+y²)
=4

（2）x+y
(x+y)²=x²+2xy+y²
=x²+xy+xy+y²
=14+2
=16
∴x+y=4或x+y=-4