(2011•内江)已知|6-3m|+(n-5)2=3m-6-(m−3)n2,则m-n=-2-2•

问题描述:

(2011•内江)已知|6-3m|+(n-5)2=3m-6-

(m−3)n2
,则m-n=-2-2•

∵|6-3m|+(n-5)2=3m-6-

(m−3)n2

∴6-3m≤0,m-3≥0,
∴m≥3,
∴已知等式化简,得(n-5)2=-
(m−3)n2

∴(n-5)2+
(m−3)n2
=0,
∴n-5=0,
n=5,
∴m-3=0,
m=3,
则m-n=3-5=-2.
故答案为:-2.