已知(x²+y²)(x²+y²-2)+1=0,求x²+y²的值
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已知(x²+y²)(x²+y²-2)+1=0,求x²+y²的值
已知(x²+y²)(x²+y²-2)+1=0,
求x²+y²的值
已知(x²+y²)(x²+y²-2)+1=0,求x²+y²的值
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
(x²+y²)(x²+y²-2)+1=0
(x²+y²)²-2(x²+y²)+1=0
(x²+y²-1)²=0
∴x²+y²=1