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# If x and n are integers and x^(n + 2) = 16x^2, what is the least possi

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Joined: 02 Sep 2009
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If x and n are integers and x^(n + 2) = 16x^2, what is the least possi  [#permalink]

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19 Feb 2019, 23:29
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65% (hard)

Question Stats:

48% (02:26) correct 52% (02:04) wrong based on 31 sessions

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If x and n are integers and $$x^{(n + 2)} = 16x^2$$, what is the least possible value of 16 + x ?

A. -16
B. -4
C. 0
D. 12
E. 16

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Re: If x and n are integers and x^(n + 2) = 16x^2, what is the least possi  [#permalink]

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19 Feb 2019, 23:50
1
$$x^{(n+2)}=16x^2$$
$$x^n.x^2=16x^2$$
$$x=0$$ or $$x^n=16$$
$$x^n=16$$ has the following solutions
$$4^2=16,(-4)^2=16,2^4=16,(-2)^4=16,16^1=16$$
Hence $$x$$ can be $$-4,-2,0,2,4,16$$ .
Least value of $$16+x=16-4=12$$
IMO C
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If x and n are integers and x^(n + 2) = 16x^2, what is the least possi  [#permalink]

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Updated on: 20 Feb 2019, 01:41
Bunuel wrote:
If x and n are integers and $$x^{(n + 2)} = 16x^2$$, what is the least possible value of 16 + x ?

A. -16
B. -4
C. 0
D. 12
E. 16

x^n*x^2=16*x^2
so
x^n=16
x=(+/-4)^2 or (+/-2)^2 , or ( 16)^1
so least value of 16+x would be at x=-4
16-4 = 12
IMO D

Originally posted by Archit3110 on 20 Feb 2019, 01:00.
Last edited by Archit3110 on 20 Feb 2019, 01:41, edited 1 time in total.
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Re: If x and n are integers and x^(n + 2) = 16x^2, what is the least possi  [#permalink]

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20 Feb 2019, 01:35
How you wrote x^2=16
when x^n*x^2=16*x^2

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Concentration: Sustainability, Marketing
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Re: If x and n are integers and x^(n + 2) = 16x^2, what is the least possi  [#permalink]

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20 Feb 2019, 01:41
mohitranjan05 wrote:
How you wrote x^2=16
when x^n*x^2=16*x^2

Posted from my mobile device

mohitranjan05 edited thanks
Re: If x and n are integers and x^(n + 2) = 16x^2, what is the least possi   [#permalink] 20 Feb 2019, 01:41
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