Question

x的平方+y的平方-2x-y+4分之5=0,求代数式x+y分之xy的值.

Answer 1

∵x²+y²-2x-y+5/4

=(x²-2x+1)+(y²-y+1/4)

=(x-1)²+(y-1/2)²

=0

又∵(x-1)²和(y-1/2)²均≥0

∴x-1=0,y-1/2=0

∴x=1,y=1/2

∴xy/(x+y)

=1×1/2÷(1+1/2)

=1/3