“若(X+Y)的2次方=7,(X-Y)的2次方=5,求XY的值.”

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“若(X+Y)的2次方=7,(X-Y)的2次方=5,求XY的值.”
“若(X+Y)的2次方=7,(X-Y)的2次方=5,求XY的值.”

“若(X+Y)的2次方=7,(X-Y)的2次方=5,求XY的值.”
(x+y)^2=7
(x-y)^2=5
(x+y)^2-(x-y)^2
=4xy=7-5
所以xy=1/2

4xy=(x+y)^2-(x-y)^2=7-5=2
xy=1/2

(X+Y)的平方-(X-Y)的平方
=4XY=2
则XY=1/2

(x+y)2=x2+y2+2xy=7
(x-y)2=x2+y2-2xy=5
(1)-(2),得4xy=2,xy=1/2