Question

Suppose C and D represent two different school populations where C > D and C and D must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary.

A: (C + D)²

B: 2(C + D)

C: C² + D²

D: C² − D²

(10 points)

Answer 1

$$C>D>0$$

$$(C+D)^2=C^2+2CD+D^2>C^2+D^2$$

$$(C+D)^2=(C+D)(C+D)>(C+D)(C-D)$$

$$=C^2-D^2$$

$$(C+D)^2-2(C+D)=(C+D)(C+D-2)$$

Therefore:

If $C+D>2,$ then

$$A: (C + D)^2$$

If $C+D<2,$ then

$$B: 2(C + D)$$