Range Question

Question

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If -3 < a < 4, and -2 < b < 2, then what is the range of (a+b)^2 ?

A) 0 ≤ (a+b)^2 < 36

B) 25 < (a+b)^2 < 36

C) -25 < (a+b)^2 < 36

D) -36 < (a+b)^2 < 25

E) o < (a+b)^2 < 36

So apparently the correct answer is A. I need some clarification.

Please explain the process. Thanks

Gh0sty15 Sep 8, 2019

CPhill · Answer 1 · 2019-09-08T04:46:57

Note that (a + b)^2 either produces a positive result or 0

So.....the least that (a + b)^2 could be is 0

And the greatest that it can be is if a ≈ 4 and b ≈ 2

So (a + b)^2 = ( ≈4 + ≈2) ^2 = (≈ 6)^2 = ≈ 36

Therefore

0 ≤ (a+b)^2 < 36