- 656 名前：１３２人目の素数さん mailto:sage [2016/07/09(土) 19:20:08.37 ID:UxNa1hu5.net]
- >>619 >>622
Soko made iwaretan-ja shooganee na…
y=log(x) は上に凸
log(LHS)
= log(a+b) + log(b+c) + log(c+a)
= 3log(2) + log[(a+b)/2] + log[(b+c)/2] + log[(c+a)/2]
≧ 3log(2) + (3/2)log[(a+b+c)/3] + (1/2){log(a)+log(b)+log(c)}
= (3/2)log(4) + (3/2)log(1/3) + (1/2)log(abc)
= (3/2)log(4/3) + (1/2)log(abc)
= log(RHS),
∴k=(4/3)^(3/2).
equality: a=b=c=1/3
