已知(x²+y²)²-y²=x²+6,求x²+y²的值
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已知(x²+y²)²-y²=x²+6,求x²+y²的值
已知(x²+y²)²-y²=x²+6,求x²+y²的值
已知(x²+y²)²-y²=x²+6,求x²+y²的值
(x²+y²)²-y²-x²-6=0
(x²+y²)²-(x²+y²)-6=0
(x²+y²-3)(x²+y²+2)=0
因为x²+y²≥0
所以x²+y²=3
(x²+y²)²-y²=x²+6
(x²+y²)²-(x²+y²)-6=0
(x²+y²-3)(x²+y²+2)=0
∴x²+y²=3 x²+y²=-2 舍去
设x2+y2=a,有源式得,a2-a=6解得,a1=3,a2=-2,所以x2+y2=3或-2
希望能帮到你,