已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2+Y^2； (2)XY.

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已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2+Y^2；(2)XY.已知(X+Y)^2=49,(X

已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2+Y^2； (2)XY.
已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2
已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2+Y^2； (2)XY.

已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2已知(X+Y)^2=49,(X-Y)^2=1,求下列各式的值:(1)X^2+Y^2； (2)XY.
(1)x^2+y^2 = [(x+y)^2+(x-y)^2]/2=[49+1]/2=25

(2)x^2+y^2+2xy=49
xy=(49-25)/2=12

25 24

(X+Y)^2=49，X^2+Y^2+2XY=49 (1)
(X-Y)^2=1, X^2+Y^-2XY=1 (2)
(1)+(2)得 2（X^2+Y^2 ）=50，
X^2+Y^2=25
（1）-（2）得4XY=48,
XY=12

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