Question

已知实数x,y,z满足x=6-y,z²=xy-9,求证：x=y

Answer 1

x=6-y
则z²=y(6-y)-9
z²+y²-6y-9=0
z²+(y-3)²=0
所以z=0,y-3=0
y=3
x=6-y=3
所以x=y

Answer 2

x=6-y,
则z²=xy-9=(6-y)y-9=-y²+6y-9=-(y-3)²
因为z²≥0，-(y-3)²≤0
所以z²=-(y-3)²=0
所以y=3
则x=6-y=3
所以x=y