已知x^2+y^2-4x+y+17\4=0,求y^-x+3xy的值.
问题描述：
已知x^2+y^2-4x+y+17\4=0,求y^-x+3xy的值.
答
x^2+y^2-4x+y+17\4=0
x^2-4x+y^2+y+4+1/4=0
（x^2-4x+4）+（y^2+y+1/4）=0
(x-2)^2+(y+1/2)^2=0
∴(x-2)^2=0 (y+1/2)^2=0
∵平方是非负数
∴x-2=0 y+1/2=0
∴x=2 y=-1/2
∴y^-x+3xy
=-1/2^-2+3×2×-1/2
=4-3
=1