作业帮设a>b>c>0 则2a^2+1/(ab)+1/(a(a-b))-10ac+25c^2的最小值是
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设a>b>c>0 则2a^2+1/(ab)+1/(a(a-b))-10ac+25c^2的最小值是
设a>b>c>0 则2a^2+1/(ab)+1/(a(a-b))-10ac+25c^2的最小值是
设a>b>c>0 则2a^2+1/(ab)+1/(a(a-b))-10ac+25c^2的最小值是
2a^2+1/(ab)+1/(a(a-b))-10ac+25c^2
=(5c-a)(5c-a)+a^2+(1/a)(1/b+1/(a-b))
>=a^2+1/(b(a-b))
=(b+(a-b))^2+1/(b(a-b))
=b^2+(a-b)^2+2b(a-b)+1/(b(a-b)) A^2+B^2>=2AB
>=2b(a-b)+2b(a-b)+1/(b(a-b))
=4b(a-b)+1/(b(a-b)) A^2+B^2>=2AB
>=4
5c=a 4b(a-b)=1/(b(a-b)) a=根号2,b=根号2/2,c=根号2/5