若xy=1,则(x+y)²-(x-y)²的值是( )

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若xy=1,则(x+y)²-(x-y)²的值是( )
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若xy=1,则(x+y)²-(x-y)²的值是( )
若xy=1,则(x+y)²-(x-y)²的值是( )

若xy=1,则(x+y)²-(x-y)²的值是( )
(x+y)²-(x-y)²
=x²+2xy+y²-(x²-2xy+y²)
=x²+2xy+y²-x²+2xy-y²
=4xy
=4*1
=4

4

4

4

原式=【(x+y)+(x-y)】【(x+y)-(x-y)】
=2x·2y=4xy
当xy=1时
4xy=4
∴原方程的值为4