09/06/11 22:25:59
>>948
e^2.302585･･･ = 10,
π = 2.302585･･･ + 0.83900･･･> 2.302585･･･ + 5/6,
e^(5/6) ≧ 1 + (5/6) + (1/2)(5/6)^2 > 1 + (5/6) + 1/3 > 2 + 1/6,
e^π > (e^2.302585)･e^(5/6) > 10･(2 + 1/6) = 21 + 2/3,
(2/5)(e^π -1) > 8 + 4/15 > 8,
>>952 下
無理筋ですた･････orz
>>953 下 (続き)
cot(A+B+C) = {1-(ab+bc+ca)}/(a+b+c-abc) =0,
より A+B+C = π/2,
(左辺) = cos(2A) + cos(2B) + cos(2C) = 1 + 4sin(A)sin(B)sin(C)
≦ 1 + 4{[sin(A)+sin(B)+sin(C)]/3}^3 (相乗･相加平均)
≦ 1 + 4{sin((A+B+C)/3)}^3 (上に凸)
= 1 + 4{sin(π/6)}^3
= 1 + 4(1/2)^3
= 3/2,