Waste less time on Facebook — follow Brilliant.

Muirhead's does not work here...

Prove that

\( \sum_{\text{sym}} 3a^4+7b^2c^2 \ge \sum_{\text{sym}} 7a^3b \)

for positive \( a, b, c \)

Note by Kaan Dokmeci
3 years ago

No vote yet
1 vote


Sort by:

Top Newest

I've been wondering whether or not I should use Muirhead at Olympiads, the same goes for Lagrange multipliers, are these viable? Of course, only if I do not see the beautiful classic inequality solution. Adrian Stefan · 3 years ago

Log in to reply

@Adrian Stefan An inequality that is true by Muirhead can be shown by a clever application of weighted AM-GM.

Lagrange Multipliers can be used but you have to be rigorous about everything, or points will be fiercely deducted. Kaan Dokmeci · 3 years ago

Log in to reply

As a hint I found this by playing around with certain expansions, namely squares. Kaan Dokmeci · 3 years ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...