- 512 名前：１３２人目の素数さん mailto:sage [2011/08/19(金) 01:38:45.69 ]
- >>509
F(A)≧ 25/4 だけなら、代数使った方が簡単....だな
A^4 + 3 = (4/√3)A^3 + (A-√3)^2 {A^2 +(2/√3)A +1}
≧ (4/√3)A^3
> (9/4) A^3,
より
F(A) - 25/4 = {(1/A^3) +3A -4} + (9/4){4A/(A^4 +3) -1}
= (A-1)^2･(3A^2 +2A+1)/A^3 - (9/4)(A-1)^2･(A^2 +2A+3)/(A^4 +3)
> (A-1)^2･{(3A^2 +2A+1) - (A^2 +2A+3)}/(A^3)
= (A-1)^2･2(A^2 -1)/(A^3)
≧ 0, (A≧1)
