Question

若x的平方+y的平方-2x-6y+10=0,求分式x的平方-y的平方/xy的值.

Answer 1

x的平方+y的平方-2x-6y+10=0

=>

x^2 - 2x + 1 -1 + y^2 - 6y + 9 - 9 + 10 =0

=>

(x-1)^2 + (y-3)^2 = 0

两个非负数的和为0

所以

x-1 = 0 且y-3=0

那么

x=1, y=3

所以(x^2-y^2)/xy = (1 - 9)/3 = -8/3