若(x+y)^2=11,(x-y)^2=7,则xy的值是多少

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若(x+y)^2=11,(x-y)^2=7,则xy的值是多少若(x+y)^2=11,(x-y)^2=7,则xy的值是多少若(x+y)^2=11,(x-y)^2=7,则xy的值是多少(x+y)^2-(x

若(x+y)^2=11,(x-y)^2=7,则xy的值是多少
若(x+y)^2=11,(x-y)^2=7,则xy的值是多少

若(x+y)^2=11,(x-y)^2=7,则xy的值是多少
(x+y)^2-(x-y)^2=4xy
4xy=4
xy=1

(x+y)^2=x^2+2xy+y^2=11
(x-y)^2=x^2-2xy+y^2=7
上式减去下式
4xy=4
xy=1

x+y)^2-(x-y)^2=4xy =11-7=4
4xy=4
xy=1

(x+y)^2-(x-y)^2=4xy
4xy=4
xy=1

1式(x+y)^2=x^2+y^2+2xy=11;2式(x-y)^2=x^2+y^2-2xy=7。用1式减去2式就得4xy=4,所以xy=1。

xy=1