x²+y²-2x-4y+5=0
x²-2x+1+y²-4y+4=0
(x-1)²+(y-2)²=0
且(x-1)²≥0,(y-2)²≥0
∴x-1=0,y-2=0
解得x=1,y=2
∴x^4+y^3
=1^4+2^3
=1+8
=9