若(x-2y)^2=5,(x+2y)^2=9,求xy的值

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若(x-2y)^2=5,(x+2y)^2=9,求xy的值
若(x-2y)^2=5,(x+2y)^2=9,求xy的值

若(x-2y)^2=5,(x+2y)^2=9,求xy的值
(x-2y)^2-(x+2y)^2=5-9
(x-2y+x+2y)(x-2y-x-2y)=-4
(2x)(-4y)=-4
-8xy=-4
xy=1/2

(x-2y)^2=5,(x+2y)^2=9,
相减得
-4xy-4xy=5-9=-4
-8XY=-4
xy=1/2

(x-2y)^2-(x+2y)^2=5-9
(x^2-2xy+4y^2)-(x^2+4xy+4y^2)=5-9
x^2-4xy+4y^2-x^2-4xy-4y^2=5-9
-8xy=5-9
-8xy=-4
xy=1/2

不懂可追问
满意请采纳
谢谢为什么是用前者减去，而不是后者(x-2y)^2-(x+2y)^2
(...

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(x-2y)^2-(x+2y)^2=5-9
(x^2-2xy+4y^2)-(x^2+4xy+4y^2)=5-9
x^2-4xy+4y^2-x^2-4xy-4y^2=5-9
-8xy=5-9
-8xy=-4
xy=1/2

不懂可追问
满意请采纳
谢谢

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