已知m,n是实数,且满足m^2+2n^2+m-3/4n+17/36=0,则-mn^2的平方根是( )
问题描述：
已知m,n是实数,且满足m^2+2n^2+m-3/4n+17/36=0,则-mn^2的平方根是( )
答
m^2+2n^2+m-4n/3+17/36=0
m^2+m+1/4+2n^2-4n/3+2/9=0
(m+1/2)^2+2(n^2-2n/3+1/9)=0
(m+1/2)^2+2(n-1/3)^2=0
满足上式的唯一条件是
m+1/2=0 m=-1/2
n-1/3=0 n=1/3
则√(-mn^2)=√[-(-1/2)(1/3)^2]=√2/6