Thread: Completely stumped on this problem!

1. 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?

2. 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?
$\displaystyle x = \pm 5$ , $\displaystyle y = \pm 4$ , and $\displaystyle z = \pm 3$

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

$\displaystyle [5 + 4 - (-3)]^2 = 12^2$

3. 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.

4. 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 ...

$\displaystyle -(-3) = +3$

5. 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

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