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题组若a,b,c∈R_+,则(1)a/(b+c)+b/(c+a)+c/(a+b)≥3/2(1963年莫斯科数学竞赛题).(2)(a~+b~)/(a+b)+(b~2+c~2)/(b+c)+(c~2+a~2)/(c+a)≥a+b+c.(3)(W.Janoux猜想)(c~2-b~2)/(a+b)+~(a~-c~2)/(b+c)+(b~2-a~2)/(c+a)≥0.(4)a~2/(b+c+b~2(c+a)+c~2/(a+b)≥(a+b+c)/3(第二届友谊杯国际数学邀请赛试题).
(A) a / b + c + b / c + a + c / a + b ≥ 3/2 if the group of a, b, c ∈ R_ + ) (2) (a ~ + b ~) / (a + b) + (b ~ 2 + c ~ 2) / (b + c) + (c ~ 2 + a ~ 2) / (c + a) ≥a + b + c (3) (W. Janoux conjecture) (c ~ 2-b ~ 2) / (a + b) + ~ (a ~ -c ~ 2) / (b + c) + A + b + 2 + c + a + c + a + 2 + a + b + 2 + a + b + c) / 3 (the second session of Friendship Cup International Mathematical Invitational test).