已知x-y=9,xy=5,求x^2+y^2怎么算?

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已知x-y=9,xy=5,求x^2+y^2怎么算?
已知x-y=9,xy=5,求x^2+y^2怎么算?

已知x-y=9,xy=5,求x^2+y^2怎么算?
x²+y²=(x-y)²+2xy=81+10=91.

x²+y²=(x-y)²+2xy=81+10=91

(x-y)^2=x^2-2xy+y^2=81
x^2+y^2=81+2xy=81+2*5=91

x-y =9 (1)
(1)两边同时平方得：x^2+y^2-2xy=81 (2)
xy=5 (3)
(3)带入（2) ，得：x^2+y^2=9-2xy=81+2*5= 91

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