已知x-y=9,xy=5 求(x+y)的平方的值

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已知x-y=9,xy=5求(x+y)的平方的值已知x-y=9,xy=5求(x+y)的平方的值已知x-y=9,xy=5求(x+y)的平方的值x-y=9两边平方x²+y²-2xy=81

已知x-y=9,xy=5 求(x+y)的平方的值
已知x-y=9,xy=5 求(x+y)的平方的值

已知x-y=9,xy=5 求(x+y)的平方的值
x-y=9
两边平方
x²+y²-2xy=81
x²+y²=81+2xy=91
所以(x+y)²
=x²+y²+2xy
=91+10
=101

(x+y)^2
=(x-y)^2+4xy
=9^2+4*5
=81+20
=101

(x+y)2=x2+2xy+y2
x-y=9
即（(x-y)2=81
∴x2-2xy+y2=81
又xy=5
∴x2+y2=76
(x+y)2=x2+2xy+y2
=76+2×(-9)
=58

(x+y)^2
=(x-y)^2+4xy
=9^2+4*5
=81+20
=101

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