The real numbers $a, b, c, d$ are such that $a\geq b\geq c\geq d>0$ and $a+b+c+d=1$. Prove that
\[(a+2b+3c+4d)a^ab^bc^cd^d<1\]
Proposed by Stijn Cambie, Belgium
IMO 2020 #2
- FuadAlAlam
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Re: IMO 2020 #2
$(a+2b+3c+4d)(a^2+b^2+c^2+d^2) \leq (a+b+c+d)^3$
Proving this is equivalent to the main problem.
Proving this is equivalent to the main problem.