Question

m.n为实数,且m^2+2n^2+m-3n/4+17/36=0则-mn^2的平方根是多少?

Answer 1

m^2+2n^2+m-4/3n+17/36=0 (m^2+m+1/4)+2(n^2-2/3n+1/9)=0 (m+1/2)^2+2(n-1/3)^2=0 平方大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立.所以两个都等于0 所以m+1/2=0,n-1/3=0 m=-1/2,n=1/3 -mn^2=-(-1/2)*1/9=1/18,平方根是:正负(根号2)/6