Question

已知(x²+y²)(x²+y²-2)+1=0,

求x²+y²的值

Answer 1

(x²+y²)(x²+y²-2)+1=0
（x²+y²)²-2(x²+y²)+1=0
(x²+y²-1)²=0
∴x²+y²=1

Answer 2

令a=x²+y²
则a(a-2)+1=0
a²-2a+1=0
(a-1)²=0
a-1=0
所以x²+y²=a=1