题目

1.xy=6,x²+y²=12,x与y相等吗?
2.x+y=6,xy=z²+9,求x,y,z的值.
3.若a-b=8,ab+c²+16=0,求证a+b+c=0.
4.若x²+2x+y²-8y+17=0,求x,y的值.

提问时间：2020-12-22

答案

1.相等y=6/x x^2+(6/x)^2=12 解得x^2=6,y^2=6 xy=6 x=y
2.x=3 y=3 z=0 x=6-y
(6-y)y=z^2+9
6y-y^2=z^2+9
y^2-6y+9+z^2=0
(y-3)^2+z^2=0
y=3,z=0
x=3
3.a=b+8
(b+8)b+c^2+16=0
b^2+8b+16+c^2=0
(b+4)^2+c^2=0
b=-4 c=0 a=4
a+b+c=0
4.x^2+2x+1+y^2-8y+16=0
(x+1)^2+(y-4)^2=0
x=-1 y=4