et $a,$ $b,$ $c$ be positive real numbers such that $a + b + c = 1.$ Find the minimum value of $a^2 + 2b^2 + c^2.$
We get minimum when a = b = c = 1/3. Minimum is (1/3)^2 + 2*(1/3)^2 + (1/3)^2 = 4/9.
