若X+Y=8,(X-Y)^2=4,则X^2+Y^2=

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若X+Y=8,(X-Y)^2=4,则X^2+Y^2=若X+Y=8,(X-Y)^2=4,则X^2+Y^2=若X+Y=8,(X-Y)^2=4,则X^2+Y^2=X+Y=8平方一下X^2+2XY+Y^2=6

若X+Y=8,(X-Y)^2=4,则X^2+Y^2=
若X+Y=8,(X-Y)^2=4,则X^2+Y^2=

若X+Y=8,(X-Y)^2=4,则X^2+Y^2=
X+Y=8 平方一下
X^2+2XY+Y^2=64 1
(X-Y)^2=X^2-2XY+Y^2=4 2
1式-2式得
4XY=64-4=60
2XY=30 3
3式代入2式得
X^2-30+Y^2=4
X^2+Y^2=34

x+y=8
x-y=2, 或 x-y=-2
x=5, y=3
或x=3, y=5
X^2+Y^2= 9+25 =34

(x+y)^2 = x^2 + 2xy + y^2 = 64 (x-y)^2 = x^2 - 2xy + y^2 = 4
2(x^2 + y^2) = 64 + 4 = 68
x^2 + y^2 = 34