已知(x+y+2)(x+y-2)=41,则√[(x-y)^2+4xy]的值为_____

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已知(x+y+2)(x+y-2)=41,则√[(x-y)^2+4xy]的值为_____
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已知(x+y+2)(x+y-2)=41,则√[(x-y)^2+4xy]的值为_____
已知(x+y+2)(x+y-2)=41,则√[(x-y)^2+4xy]的值为_____

已知(x+y+2)(x+y-2)=41,则√[(x-y)^2+4xy]的值为_____
即(x+y)²-4=41
(x+y)²=45
所以 （x-y)²+4xy
=x²-2xy+y²+4xy
=x²+2xy+y²
=(x+y)²
所以原式=|x+y|=3√5

3√5.

(x+y+2)(x+y-2)=41
(x+y)²-4=41
(x+y)²=45

x²+2xy+y²=45


（x-y)²+4xy
=x²-2xy+y²+4xy

=x²+2xy+y²=45

√45=3√5

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