Two numbers have a difference of 20. When the squares of the numbers are added together, the result is a minimum. What is the larger of the two numbers?

Question

I have no idea how to get to the answer, please help! Thank you.

Answer 1

Here are some hints:  

 

You are looking for 2 numbers.  Call them X and Y.  If their difference is 20, then X - Y = 20.  Solving this equation for Y gives Y = X - 20.  

 

You want to minimize the sum of X² + Y² which can be written as X² + (X-20)².  Multiplying this out will give you a quadratic which opens upward.  The minimum value of the quadratic occurs at the vertex.