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If n is an integer and square_root(n^2-6n+9)=5, which of the ...

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If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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New post 08 Aug 2018, 08:43
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A
B
C
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Difficulty:

  35% (medium)

Question Stats:

65% (01:40) correct 35% (01:27) wrong based on 54 sessions

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If n is an integer and \(\sqrt{(n^2-6n+9)}\)=5, which of the following could be the value of \((n + 3)^2\)?

A) –2
B) 1
C) 4
D) 11
E) 64

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If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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New post 08 Aug 2018, 09:00
1
CAMANISHPARMAR wrote:
If n is an integer and \(\sqrt{(n^2-6n+9)}\)=5, which of the following could be the value of \((n + 3)^2\)?

A) –2
B) 1
C) 4
D) 11
E) 64


\(n^2-6n+9\) can be written as \((n-3)^2\)

Given, \(\sqrt{(n^2-6n+9)}\)=5
Squaring both sides, we have

\(n^2-6n+9=5^2\)
Or, \((n-3)^2=5^2\)
Or, \(|n-3|=5\)
So, n-3=5 or, n-3=-5
So, n=8 or, -2

Now, \((n+3)^2=(-2+3)^2=1^2=1\)
Or, \((n+3)^2=(8+3)^2=11^2=121\) (not in answer options)

Ans. (B)
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Re: If n is an integer and square_root(n^2-6n+9)=5, which of the ...  [#permalink]

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New post 09 Aug 2018, 02:52
1. square both sides.
2.find x, which will be either 8 or -2.
3.substitute value, comes either 121 or 1.

4. 1 is correct answer.
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Re: If n is an integer and square_root(n^2-6n+9)=5, which of the ... &nbs [#permalink] 09 Aug 2018, 02:52
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