已知m²+2n²+2p²-2mn-2np-6p+9=0,求m分之n²p

已知m²+2n²+2p²-2mn-2np-6p+9=0,求m分之n²p
已知m²+2n²+2p²-2mn-2np-6p+9=0,求m分之n²p

已知m²+2n²+2p²-2mn-2np-6p+9=0,求m分之n²p
m²+2n²+2p²-2mn-2np-6p+9=0
m²-2mn+n²+p²-6p+9+n²-2np+p²=0
(m-n)^2+(p-3)^2+(n-p)^2=0
(m-n)^2=0,m=n
(p-3)^2=0,p=3
(n-p)^2=0,n=p
所以
m=n=p=3
m分之n²p
=27除以3
=9

m²+2n²+2p²-2mn-2np-6p+9=0
（m²-2mn+n²）+（n²-2np+p²）+（p²-6p+9）=0
（m-n）²+（n-p）²+（p-3）²=0
所以，m=n=p=3
所以，m分之n²p=3分之（3²×3）=9

m²+2n²+2p²-2mn-2np-6p+9=0=m²-2mn+n^2+n²-2np+p²+p^2-6p+9=(m-n)^2+(n-p)^2+(p-3)^2
所以m=n=p=3
所以n^2p/m=m^2=9