Minimum possible sum of squares of two numbers with sum $k$? If the sum of two numbers is k. Find the minimum value of the sum of their squares.
This is my calculations so far.
a + b = k                <-- google says that I should put x + y = k rather than a + b = k
a² + b² = y                  (but I don't know why should I do that)
(k - b)² + b² = y
k² - 2kb + 2b² = y       <-- now I'm stuck here. I don't know which differentiation variable to take. If it is 'b' then why?

So here I am. Kindly show me how to solve the problem and where did I go wrong in my computations :P

Hint: $x^2+y^2 \ge \dfrac{(x+y)^2}{2}$.
