已知x,y满足x^2+y^2-6x+8y+25=0,求y^x的值

问题描述:

已知x,y满足x^2+y^2-6x+8y+25=0,求y^x的值

(x²-6x+9)+(y²+8y+16)=0
(x-3)²+(y-4)²=0
x-3=0且y-4=0
则:x=3、y=4
则:y^x=4^3=64

x^2+y^2-6x+8y+25=0
(x-3)²+(y+4)²+0
素以
x-3=0 x=3
y+4=0 y=-4
y^x=(-4)^3=-64

x^2+y^2-6x+8y+25=0
x²-6x+9+y²+8y+16=0
(x-3)²+(y+4)²=0
x-3=0
x=3
y+4=0
y=-4
y^x
=-4³
=-64