已知实数x、y满足(x²+y²)(x²+y²-1)=2,试求x²+y²
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已知实数x、y满足(x²+y²)(x²+y²-1)=2,试求x²+y²
已知实数x、y满足(x²+y²)(x²+y²-1)=2,试求x²+y²
已知实数x、y满足(x²+y²)(x²+y²-1)=2,试求x²+y²
设x²+y²=M,则
M(M-1)=2
M²-M-2=0
(M-2)(M+1)=0
M-2=0或M+1=0
M=2或M=-1
x²+y²=2或x²+y²=-1(不合,舍去)
整体法:
设x^2+y^2=A
A(A-1)=2
A^2-A-2=0
(A+1)(A-2)=0
A+1=0或A-2=0
A=-1或2
x²+y²=-1(舍去)或x²+y²=2
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