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Suppose A and B represent two different school populations where A>B and A and B must be greater then 0. Which of the following expressions is the largest? Explain why. Show all work necessary.
A:2(A+B)
B:(A+B)^2
C:A^2+B^2
D:A^2-B^2

Respuesta :

Answer:

Option: B is correct

Step-by-step explanation:

We know that A and B represents two different school populations.

Hence, A and B will be a positive integer.

Also we are given A>B

Since,

[tex](A+B)^2=A^{2}+B^2+2AB[/tex]

⇒ [tex](A+B)^2>A^2+B^2[/tex] ( As 2AB is a positive quantity)

Also [tex]A^2+B^2>A^2-B^2[/tex]

Since an positive quantity [tex]B^2[/tex] added to [tex]A^2[/tex] will make the term greater than an positive quantity [tex]B^2[/tex] subtracted from [tex]A^2[/tex].

 Also [tex](A+B)^2>2(A+B)[/tex]

(Since [tex]n^2>2n[/tex] for all n>2)

Hence the largest term among all the terms is [tex](A+B)^2[/tex].

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