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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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New post Updated on: 03 Oct 2017, 05:15
2
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25
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A
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D
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Question Stats:

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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

Originally posted by maxx1234 on 28 Dec 2015, 00:53.
Last edited by Bunuel on 03 Oct 2017, 05:15, edited 2 times in total.
Added the OA.
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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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New post 28 Dec 2015, 02:19
2
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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New post 15 May 2016, 08:29
2
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.

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

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New post 22 Mar 2019, 09:21
1
One could try and substitute values.

if x=1 the expression (x^2+9/x^2) = 10
if x=2, 4+(9/4)=6.25
if x=3, 10
if x=4, 16&9/16
if x=5, 25&9/25
if x=6 36&1/4

We want the expression to =31 so x=5.5 is a good estimate.

x-3/x=

5.5-(3/5.5)=

5.5 - (little more than .5)=close to 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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New post 22 Mar 2019, 10:42
1
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 \(a\) = the correct answer.

\(x - \frac{3}{x}=a\)

Since \((m-n)^2 = m^2 + n^2 - 2mn\), squaring both sides yields the following:
\((x - \frac{3}{x})^2=a^2\)

\(x^2 - \frac{9}{x^2} - 2(x)(\frac{3}{x})=a^2\)

\(x^2 - \frac{9}{x^2} - 6=a^2\)

Substituting \(x^2 + \frac{9}{x^2} = 31\) into the resulting blue equation, we get:
\(31 - 6=a^2\)

\(25 = a^2\)

±\(5=a\)


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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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New post 28 Dec 2015, 02:29
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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New post 28 Dec 2015, 02:32
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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New post 15 May 2016, 08:12
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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New post 15 May 2016, 08:59
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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New post 15 May 2016, 09:41
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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New post 15 May 2016, 09:44
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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New post 05 Oct 2017, 10:13
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1
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.

Answer: 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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New post 13 Jun 2018, 05:41
ScottTargetTestPrep wrote:
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.

Answer: D



Hey pushpitkc,

can you shed some light on the solution above ..i dont get the steps (highlighted) after this "Since x^2 + 9/x^2 = 31"

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

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New post 13 Jun 2018, 08:09
1
dave13

You can convert any a^2+b^2 to a^2+b^2-2ab+2ab=(a-b)^2+2ab
x^4 + 9/x^2 = x^4 + 9/x^2 - 2*(x^2 *3/x^2) + 2*(x^2 *3/x^2)
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If x^2 + 9/x^2 = 31, what is the value of x - 3/x?  [#permalink]

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New post 13 Jun 2018, 12:25
1
dave13 wrote:
ScottTargetTestPrep wrote:
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.

Answer: D



Hey pushpitkc,

can you shed some light on the solution above ..i dont get the steps (highlighted) after this "Since x^2 + 9/x^2 = 31"

many thanks :-)


Hey dave13

We are given \(x^2 + \frac{9}{x^2} = 31\) in the queston stem -> Lets call this equation (1)

Once, we have squared the equation, \((x - \frac{3}{x})^2\) to get \(x^2 - 6 + \frac{9}{x^2}\)

After re-arranging \((x - \frac{3}{x})^2 = x^2 + \frac{9}{x^2} - 6 = 31 - 6 = 25\) [from equation (1)]

Now, \((x - \frac{3}{x})^2 = 25\) -> \((x - \frac{3}{x}) = \sqrt{25} = +5\) or \(-5\)

Therefore, the answer option which matches the value of \((x - \frac{3}{x})\) is 5(Option D)

Hope this helps you
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If x^2 + 9/x^2 = 31, what is the value of x - 3/x?   [#permalink] 13 Jun 2018, 12:25
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