Question

已知x^2+y^2=5 xy=2 计算:(1) (x+y)^2 (2) x-y (3) x^4+y^4

Answer 1

x^2+y^2=5,xy=2

(x+y)^2=x^2+y^2+2xy=5+2*2=9

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

∴（1）(x+y)^2=9

（2）x-y=±1

（3）x^4+y^4=(x^2+y^2)^2-2x^2y^2

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

=5^2-2*2^2

=25-8

=17