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# Range 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.

Sep 8, 2019

#1
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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   Sep 8, 2019
#2
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Ah thanks CPhill. You've been saving me for the past few questions. I really appreciate it.

Just a quick follow up. Can you explain why it can't be option B?

Gh0sty15  Sep 8, 2019
edited by Gh0sty15  Sep 8, 2019
#3
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It can't be "B"  because we need the entire  range possible  of  (a+b)^2

"B"  says  that   (a + b)^2   must be  >  25    [ but   < 36 ]

But this isn't  true......note  if   a = 0   and  b  = 0....then (a + b)^2  = (0 + 0)^2  =  0

So....we can make   (a +b)^2   less than 25   CPhill  Sep 8, 2019