设a>b>c>0,则2a^2+1/ab+1/a(a-b)-10ac+25c^2的最小值b(a-b)

设a>b>c>0,则2a^2+1/ab+1/a(a-b)-10ac+25c^2的最小值b(a-b)
设a>b>c>0,则2a^2+1/ab+1/a(a-b)-10ac+25c^2的最小值
b(a-b)

设a>b>c>0,则2a^2+1/ab+1/a(a-b)-10ac+25c^2的最小值b(a-b)
由b(a-b)=a^2+4/a^2+(a-5c)^2
>=4
等号成立当且仅当b=a-b,a=5c,a^=2.

2a^2+1/ab+1/a(a-b)-10ac+25c^2
=a^2-10ac+25c^2+a^2+1/ab+1/a(a-b)
=(a-5)^2+(ab+1/ab)-ab+a^2+1/a(a-b)
>=(a-5)^2+2*根号(ab*1/ab)-a(a-b)+1/a(a-b)=0+2+2=4
当且仅当ab=1/ab和a(a-b)=1/a(a-b)时