If $a,b,c\in\mathbb{R}$ and $2a+b+3c=20.$ Then minimum value of $a^2+4b^2+c^2$ is
what i try
Cauchy schwarz inequality
$$(a^2+(2b)^2+c^2)(2^2+\frac{1}{2^2}+3^2)\geq (2a+b+3c)^2$$
How do i solve it without Cauchy schwarz inequality Help me please
Minimum of $a^2+4b^2+c^2$ given $2a+b+3c=20$
inequalitymaxima-minimaoptimizationquadratics
Best Answer
An alternative way of solving the problem is using Lagrange multipliers, other than that (i.e. without using the CS inequality), I don't see a simple solution, and neither do I see a reason to look for such a solution.