Two numbers have a sum of 13 (terminology & help)

[Monocerotis]

Homework Statement

10) Two numbers have a sum of 13.
10)a) Find the minimum of the sum of their squares.
10)b) What are the two numbers

Homework Equations

y=ax²+bx+c
y=a(x-h)²+k

According to the text: for a quadratic function in the forum of y=a(x-h)²+k, the maximum or minimum value is k, when x=h. If a> 0, k is the minimum value of the function. If a <0, k is the maximum value of the function.

The Attempt at a Solution

No attempt, do not understand how to properly attempt the question.

What I believe to understand is that
a) the question is asking for the value of two numbers which add up to 13, and
b) what the value of those two numbers squared, then added up together is. I don't understand why it's asking for the "minimum" value of their squares.

 

[flatmaster]

Two numbers have the sum of 13

a+b = 13

The sum of their squares is

y = a^2 + b^2

How could you find the minimum of this sum?

 

[Monocerotis]

Two numbers have the sum of 13


How could you find the minimum of this sum?

No idea, hence the thread lol.

 

[Bohrok]

I would understand "Minimum of the sums of their squares" to be the smallest number, or minimum number, that their squares add up to.
What about writing the two numbers as x and 13-x? Then add their squares and minimize that function.

 

[Monocerotis]

I would understand "Minimum of the sums of their squares" to be the smallest number, or minimum number, that their squares add up to.
What about writing the two numbers as x and 13-x? Then add their squares and minimize that function.

Ok, so how do you go about finding what those two numbers are ?

 

[Bohrok]

Once you find what x is (one of the numbers), subtract it from 13 to get the other (13-x in my last post).

 

[Monocerotis]

Once you find what x is (one of the numbers), subtract it from 13 to get the other (13-x in my last post).

how do you find x ?

 

[Bohrok]

Let x and 13-x be the two numbers. Create a function that squares each of these numbers and adds them together. Can you do that?
Then find the minimum of the function.