x-2y=12,xy=-25,求x^2+4y^2-1的值

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x-2y=12,xy=-25,求x^2+4y^2-1的值
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x-2y=12,xy=-25,求x^2+4y^2-1的值
x-2y=12,xy=-25,求x^2+4y^2-1的值

x-2y=12,xy=-25,求x^2+4y^2-1的值
∵x-2y=12
将两边同时平方
（x-2y）²=12²
展开
x²-4xy+4y²=144
∵x²+4y²=144+4xy
∴x²+4y²-1=143+4xy
∵xy=-25
∴x²+4y²-1=143+4·-25=43
希望满意采纳.

x^2+4y^2-1
=x²-4xy+4y²+4xy-1
=(x-2y)²+4xy-1
=12²+4*(-25)-1
=144-100-1
=43

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