x^2+y^2-4x+y+174=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
x^2+y^2-4x+y+174=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