Question

已知x-y=2,x^2+y^2=4,求x^2004+y^2004的值.

Answer 1

x-y=2 平方

x^2-2xy+y^2=4

xy=0

x-y=2

x=2+y

(2+y)*y=0

y=0或y=-2

x=2或x=0

所以

x^2004+y^2004

=0^2004+(±2)^2004

=2^2004