exercise 7 for inequality

[S]【YU】

sqrt (ab) <= (a+b)/2
ab <= (a+b)^2/4
abc <= (a+b)^2/4            (0 <= c <= 1)
abc(a+b) <= (a+b)^3/4
abc(1-c) <= (a+b)^3/4

abc <= (a+b+c)^3/27 = 1/27
27abc <= 1
(27abc - c^3)/(a+b) = (1-c^3)/(1-c) = c^2 + c + 1 <= 1/9 + 1/3 + 1 <= 13/9