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If x^2 + 9/x^2 = 31, what is the value of x - 3/x?

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If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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27 Dec 2015, 23:53
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If $$x^2 + \frac{9}{x^2} = 31$$, what is the value of $$x - \frac{3}{x}$$?

A. 36
B. 25
C. 9
D. 5
E. 3
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Oct 2017, 04:15, edited 2 times in total.

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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28 Dec 2015, 01:19
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option D.

To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (31) - 2*3 = 25
=> t^2 = 25. Thus t=5 or t=-5.

=> option D.
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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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28 Dec 2015, 01:29
Dont get this part

- 2*x*3/x

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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28 Dec 2015, 01:32
maxx1234 wrote:
Dont get this part

- 2*x*3/x

Have just used the formula (a-b)^2 = a^2 + b^2 - 2*a*b.
Here a is x and b is 3/x.

Consider Kudos if this helps.
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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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15 May 2016, 07:12
ritikk13 wrote:
maxx1234 wrote:
Dont get this part

- 2*x*3/x

Have just used the formula (a-b)^2 = a^2 + b^2 - 2*a*b.
Here a is x and b is 3/x.

Consider Kudos if this helps.

Hi ritikk,

if x-3/x is squared then resultant equation after substitution will be 31 - (6/x). How do you arrive at 5 from this when x is still present?

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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15 May 2016, 07:29
Expert's post
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Senthil7 wrote:
ritikk13 wrote:
maxx1234 wrote:
If x^2 + 9/x^2 = 31, what is the value of x - 3/x

A 36
B 25
C 9
D 5
E 3

Dont get this part

- 2*x*3/x

Have just used the formula (a-b)^2 = a^2 + b^2 - 2*a*b.
Here a is x and b is 3/x.

Consider Kudos if this helps.

Hi ritikk,

if x-3/x is squared then resultant equation after substitution will be 31 - (6/x). How do you arrive at 5 from this when x is still present?

$$(x-\frac{3}{x})^2=x^2-2*x*\frac{3}{x}+(\frac{3}{x})^2=x^2-6+\frac{9}{x^2}$$

Since $$x^2 + \frac{9}{x^2} = 31$$, then $$(x-\frac{3}{x})^2=x^2-6+\frac{9}{x^2}=31-6=25$$.

Finally, $$(x-\frac{3}{x})^2=25$$ --> $$x-\frac{3}{x}=5$$ or -5.

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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15 May 2016, 07:59
very nice question but needs smart eyes to catch the idea.
Are there any alternate approach ?

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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15 May 2016, 08:41
Bunuel thanks a lot. The misunderstanding is due to the font type not sure if it was x-3 the whole term by x or just x minus 3/x. That issue with members posting can solve the issue i think any way out or any suggestion like you have typed now appropriately? Bunuel

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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15 May 2016, 08:44
Senthil7 wrote:
Bunuel thanks a lot. The misunderstanding is due to the font type not sure if it was x-3 the whole term by x or just x minus 3/x. That issue with members posting can solve the issue i think any way out or any suggestion like you have typed now appropriately? Bunuel

Mathematically x - 3/x can only mean x minus 3/x. If it were x-3 over x it would e written as (x - 3)/x.
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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x? [#permalink]

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05 Oct 2017, 09:13
maxx1234 wrote:
If $$x^2 + \frac{9}{x^2} = 31$$, what is the value of $$x - \frac{3}{x}$$?

A. 36
B. 25
C. 9
D. 5
E. 3

Let’s square x - 3/x first:

(x - 3/x)^2 = x^2 - 6 + 9/x^2

Since x^2 + 9/x^2 = 31, we have x^2 - 6 + 9/x^2 = 31 - 6 = 25.

So, (x - 3/x)^2 = 25 and:

x - 3/x = ±5

We see that only 5 is among the answer choices.

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Re: If x^2 + 9/x^2 = 31, what is the value of x - 3/x?   [#permalink] 05 Oct 2017, 09:13
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