Completely stumped on this problem!

• Oct 13th 2009, 04:27 PM
freddy
Completely stumped on this problem!
If x squared = 25, y squared = 16, and z squared = 9 what is the greatest possible value of (x + y - z)squared?

My book says the answer is 144. Can someone please tell me how that the book got this answer?
• Oct 13th 2009, 04:34 PM
skeeter
Quote:

Originally Posted by freddy
If x squared = 25, y squared = 16, and z squared = 9 what is the greatest possible value of (x + y - z)squared?

My book says the answer is 144. Can someone please tell me how that the book got this answer?

$x = \pm 5$ , $y = \pm 4$ , and $z = \pm 3$

you want x , y , and -z to all have the same sign to maximize the square

$[5 + 4 - (-3)]^2 = 12^2$
• Oct 13th 2009, 04:48 PM
freddy
how?
How can you make the 3 negative if its positive in the problem? You have 2 minus signs yet there is only 1 minus sign in the problem.
• Oct 13th 2009, 04:50 PM
skeeter
Quote:

Originally Posted by freddy
How can you make the 3 negative if its positive in the problem? You have 2 minus signs yet there is only 1 minus sign in the problem.

freddy ...

$-(-3) = +3$
• Oct 13th 2009, 04:55 PM
gs.sh11
When you take the square root of any number such as 25 a negative can also be the solution, for example (-5)(-5) = 25, as (5)(5) = 25, so x = -5, y = -4, and because the equation is (x + y - z), z = 3, so now

$(-5 - 4 - 3)^2 = 144$