Completing the square?

[Courtneydb]

I'm not sure if this is in the right forum, I hope it is. If not, I'm sorry.

I am really not sure how to do this question, and I didn't learn it in class. Our unit right now is 'completing the square', which, as far as I can tell, is mainly just solving word problems using algebra, but using the equation of a parabola (vertex form: y=a(x-h)²+k).

The sum of two numbers is 26. The sum of their squares is a minimum. Find the numbers.

So far, I don't actually have anything, aside from x+y=26.

 

[tkhunny]

The sum of their squares is a minimum.

\(\displaystyle x^{2} + y^{2}\)

Given that x + y = 26, what can you do with that expression?

 

[mmm4444bot]

Yes, this is an intermediate-algebra exercise.

x + y = 26 is a fine start.

Solve this for y, to obtain an expression for y in terms of x.

Use this expression to represent the number y.

Next, write the sum of the square of each number. This should yield a quadratic polynomial in x.

The minimum sum is located at the vertex of the parabola.

Does this information help you to continue?