Question

已知x-y不等于0,x^2+y=21,x+y^2=21,求（x+y）^2101

Answer 1

x^2+y=21

x+y^2=21

两式相减得

(x-y)(x+y)-(x-y)=0

(x-y)(x+y-1)=0

x-y不等于0,

x+y-1=0

x+y=1

（x+y）^2101=1