Suppose X and Y represent two different school populations where X Y and X and Y must be greater than 0. Which of the following expressions is the largest?

X2 + Y2
X2 − Y2
2(X + Y)
(X + Y)2

Question

Suppose X and Y represent two different school populations where X > Y and X and Y must be greater than 0. Which of the following expressions is the largest? 


X2 + Y2
X2 − Y2
2(X + Y)
(X + Y)2

anonymous · Answer

Would you simply assign a value to each of the variables, say x=2 and y=1, and simply show the work for the output of each expression??

irishboy123 · Answer

great idea to plug in some values to start with

so smallest numbers are $X, Y = 1,1$  -- which sounds pretty dumb for a school population *but* you are only told that $X,Y > 0,0 $-- and no more info is provided.  and, as you don't usually get half a teacher or half a student, you have started with $X,Y = 1,1$;  in which case the options evaluate as $ 2,0,4,4$

you can do the same for $X,Y = 1, 2 $ and $ X, Y = 2,1$, and see how it pans out

thereafter, if you next move onto more realistic assumption that $X, Y \geq 2$, you know that  $X^2, Y^2 \gt X,Y > 4,4$ ad you can start to compare these properly using alebra alone

not sure you're going to get a very satisfactory answer from this