已知x+y=5 xy=3 求(x-y)^2

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已知x+y=5 xy=3 求(x-y)^2
已知x+y=5 xy=3 求(x-y)^2

已知x+y=5 xy=3 求(x-y)^2
x+y=5
两边平方
x^2+2xy+y^2=25
x^2+y^2=25-2xy=19
所以(x-y)^2
=x^2-2xy+y^2
=19-6
=13

(x+y)^2=x^2+y^2+2xy=25,所以(x-y)^2=x^2+y^2-2xy=25-4*3=13

答案：因为x+y=5,xy=3,(x-y)^2=(x+y)^2-4xy
所以原式=5^2-4x3=13.

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