已知xy是实数且(x+y-1)^2与|2x-y+4|互为相反数,求实数y^x的负倒数

Question

已知xy是实数且(x+y-1)^2与|2x-y+4|互为相反数,求实数y^x的负倒数

Answer 1

(x+y-1)^2与|2x-y+4|互为相反数,
(x+y-1)^2>=0,|2x-y+4|>=0,互为相反数
则
x+y-1=0;
2x-y+4=0
3y=6
y=2,x=-1
y^x=2^(-1)=1/2,y^x的倒数=2,y^x的负倒数=-2.