Question 4
Prove that for all positive real numbers $a,b,c$,
$$\frac{a^3}{(a+b)^3}+\frac{b^3}{(b+c)^3}+\frac{c^3}{(c+a)^3}\ge\frac38.$$
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.
$$\frac{a^3}{(a+b)^3}+\frac{b^3}{(b+c)^3}+\frac{c^3}{(c+a)^3}\ge\frac38.$$
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.