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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

Respuesta :

keonabadona
The question or the problem wants to choose among the following expression is the largest, base on the data presented in the problem, the possible answer among the following choices is C2+D2.  I hope this helps :D
botellok

Answer:

A.

Step-by-step explanation:

We have that C>0, D>o and C > D. Now,

A. [tex](C+D)^2= C^2+2CD+D^2[/tex]

B. 2(C+D) = 2C+2D

C. [tex]C^2+D^2[/tex]

D. [tex]C^2-D^2[/tex]

We have that [tex]C^2+2CD+D^2> C^2+D^2[/tex] (beacuse on left we have adding one extra positive term) and also [tex]C^2+D^2> C^2-D^2[/tex] (adding two positive values is greater than subtract two positive values), then

[tex]C^2+2CD+D^2> C^2-D^2[/tex]

also, [tex]C^2+2CD+D^2> 2C+2D[/tex] (also because the middle term). Then, the largest term is  [tex](C+D)^2= C^2+2CD+D^2[/tex].

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