已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值

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已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值
已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值

已知(x+y)^2=25,(x-y)^2=9,求xy与x^2+y^2的值
(x+y)²=25
(x-y)²=9
展开得
x²+2xy+y²=25
x²-2xy+y²=9
化为
(x²+y²)+2(xy)=25
(x²+y²)-2(xy)=9
两式相加得
2(x²+y²)=34
x²+y²=17,所以xy=4

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

(x+y)^2=x^2+2xy+y^2=25......(1)
(x-y)^2=x^2-2xy+y^2=9......(2)
[(1)+(2)]/2=>x^2+y^2=17
[(1)-(2)]/4=>xy=4

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

xy=4;x^2+y^2=17

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