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# If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is

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Joined: 25 Jan 2016
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Location: India
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If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is  [#permalink]

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23 Jun 2017, 13:12
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00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:05) correct 51% (02:59) wrong based on 99 sessions

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If 2p/(p^2-2p+1) = 1/4, then the value of p+1/p is

A) 8
B) 10
C) 12
D) 2√6
E) None of these
Math Expert
Joined: 02 Sep 2009
Posts: 52231
If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is  [#permalink]

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23 Jun 2017, 22:38
1
aveek86 wrote:
If 2p/(p^2-2p+1) = 1/4, then the value of p+1/p is

A) 8
B) 10
C) 12
D) 2√6
E) None of these

$$p+\frac{1}{p}=\frac{p^2+1}{p}=?$$

Given:
$$\frac{2p}{(p^2-2p+1)} = \frac{1}{4}$$

$$4*2p = p^2-2p+1$$

$$p^2 + 1 = 10p$$

Thus:
$$p+\frac{1}{p}=\frac{p^2+1}{p}=\frac{10p}{p}=10$$.

Hope it helps.
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If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is  [#permalink]

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24 Jun 2017, 00:52
Given $$\frac{2p}{(p^2-2p+1)} = \frac{1}{4}$$ Now, $$(p^2-2p+1) = 8p$$ --> 1

Now, since we are asked to find out the value of $$p+\frac{1}{p}$$
$$p+\frac{1}{p}$$ = $$\frac{p^2 + 1}{p}$$

$$\frac{p^2 + 1}{p}$$ = $$\frac{p^2 + 1+ 2p - 2p}{p}$$ (Adding & subtracting 2p to the numerator of the expression)
= $$\frac{p^2 + 1 - 2p}{p} + \frac{2p}{p}$$
Substituting the value of $$p^2 + 1 - 2p$$ from 1,
= $$\frac{8p}{p} + 2$$ = 10(Option B)
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Re: If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is  [#permalink]

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24 Jun 2017, 03:01
p + 1/p = p^2 + 1/p

8p = p^2 - 2p + 1
p^2 - 2p + 1 - 8p = 0
p^2 - 10p + 1 = 0

p^2+1 = 10p

p^2+1/p = 10p/p = 10. Ans - B.
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If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is  [#permalink]

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24 Jun 2017, 09:30
1
Interesting question, easy but could be missed if overthought. I think the trick is not to solve for p first but try to isolate the whole p+1/p. Cross multiplication gives p^2 - 10p + 1 = 0 ; p^2 + 1 = 10p ; p+1/p=10

In summary, collect like times and try to get rid of the exponent on p. Also, a familiarity with the form p+1/p as quadratic will help see the connection.
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Re: If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is  [#permalink]

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29 Oct 2018, 22:54
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Re: If 2p/(p^2-2p+1) =1/4, then the value of p+1/p is &nbs [#permalink] 29 Oct 2018, 22:54
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