Question 57
Prove that for all real $a,b,c\gt 0$ and every real $t\ge0$,
$$\frac{a}{b+tc}+\frac{b}{c+ta}+\frac{c}{a+tb}\ge\frac3{1+t}.$$
$$\frac{a}{b+tc}+\frac{b}{c+ta}+\frac{c}{a+tb}\ge\frac3{1+t}.$$
MathNet 2012 Question 57
Math Olympiad Vault · MathNet 2012