Question

已知：x的平方+2xy=-4,2xy+y的平方=8求下列代数式的值；（1）x的平方+4xy+y的平方；(2)x的平方-y

Answer 1

x^2+2xy=-4

2xy+y^2=8

(1)x^2+4xy+y^2

=(x^2+2xy)+(2xy+y^2)

=-4+8

=4

(2)x^2-y^2

x^2+2xy=-4 ①

2xy+y^2=8 ②

①-②得

x^2-y^2=-12