已知(x+y)(x+y)=25,(x-y)(x-y)=9求xy与xx+yy的值

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已知(x+y)(x+y)=25,(x-y)(x-y)=9求xy与xx+yy的值已知(x+y)(x+y)=25,(x-y)(x-y)=9求xy与xx+yy的值已知(x+y)(x+y)=25,(x-y)(

已知(x+y)(x+y)=25,(x-y)(x-y)=9求xy与xx+yy的值
已知(x+y)(x+y)=25,(x-y)(x-y)=9求xy与xx+yy的值

已知(x+y)(x+y)=25,(x-y)(x-y)=9求xy与xx+yy的值
(x+y)(x+y)=25
x^2+2xy+y^2=25……(1)
(x-y)(x-y)=9
x^2-2xy+y^2=9……（2）
（1）+（2）得：
2x^2+2y^2=34
x^2+y^2=17
(1)-(2)得：
4xy=16
xy=4

xy=[(x+y)(x+y)-(x-y)(x-y)]/4=(25-9)/4=4
xx+yy=[(x+y)(x+y)+(x-y)(x-y)]/2=(25+9)/2=17

4 17

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