Question

若x,y满足x的平方+y的平方=5/4,xy=-1/2,求x的平方-y的平方

Answer 1

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

(x+y)^2=x^2+y^2+2xy=5/4-1=1/4

x+y=+-1/2

(x-y)^2=x^2+y^2-2xy=5/4+1=9/4

x-y=+-3/2

x^2-y^2=3/4或-3/4