函数y=alg(x-2)+1的图像恒过定点A(3,1),
点A在直线mx+ny-1=0上,所以3m+n=1.
3/m+1/n=(3m+n)/m+(3m+n)/n
=3+n/m+3m/n+1
=4+ n/m+3m/n≥4+2√(n/m•3m/n)= 4+2√3