# Functions question

• Mar 8th 2009, 09:28 PM
demo1
Functions question
Hi, here's a problem that I don't quite understand:

"The sum of two numbers is 26, the sum of their squares is a minimum. Determine the two numbers."

How would i model the 2 numbers? Is this correct? X^2 + (26-X)^2 = 0? What does it mean by the sum of their squares is a MINIMUM? What would the equation look like if the sum of their squares was a MAXIMUM?

Thanks.
• Mar 8th 2009, 11:12 PM
u2_wa
Quote:

Originally Posted by demo1
Hi, here's a problem that I don't quite understand:

"The sum of two numbers is 26, the sum of their squares is a minimum. Determine the two numbers."

How would i model the 2 numbers? Is this correct? X^2 + (26-X)^2 = 0? What does it mean by the sum of their squares is a MINIMUM? What would the equation look like if the sum of their squares was a MAXIMUM?

Thanks.

Open this equation:
$x^2 + (26-x)^2$
You will get
$679 + 2x^2 - 52x
$
, Now you can either take it's derivative and equate it to zero to get the value of x where this function is minimum or express it in the form of $a(x-c)^2+d$ and equate $(x-c)=0$ and get the value of x i.e $c$