已知a>0,b>0a+b=2则y=1/a+4/b的最小值如题

Question

已知a>0,b>0 a+b=2则y=1/a+4/b的最小值
如题

Answer 1

(a+b)/2=1
suoyi
1/a+4/b
=[(a+b)/2](1/a+4/b)
=1/2(a+b)(1/a+4/b)
=1/2[5+(b/a+4a/b)]>=1/2[5+2genhao(b/a*4a/b)]
yinwei a+b=2
souyi zuixiaozhi = 4.5