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If x^2 + 9/x^2 = 31, what is the value of x  3/x?
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Updated on: 03 Oct 2017, 05:15
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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
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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?
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28 Dec 2015, 02:19
option D. To find : x3/x. Let it be t. => x3/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?
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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?
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28 Dec 2015, 02:32
maxx1234 wrote: Dont get this part
 2*x*3/x Have just used the formula (ab)^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?
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15 May 2016, 08:12
ritikk13 wrote: maxx1234 wrote: Dont get this part
 2*x*3/x Have just used the formula (ab)^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 x3/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?
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15 May 2016, 08:29
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 (ab)^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 x3/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? \((x\frac{3}{x})^2=x^22*x*\frac{3}{x}+(\frac{3}{x})^2=x^26+\frac{9}{x^2}\) Since \(x^2 + \frac{9}{x^2} = 31\), then \((x\frac{3}{x})^2=x^26+\frac{9}{x^2}=316=25\). Finally, \((x\frac{3}{x})^2=25\) > \(x\frac{3}{x}=5\) or 5. Answer: D.
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Re: If x^2 + 9/x^2 = 31, what is the value of x  3/x?
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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?
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15 May 2016, 09:41
Bunuel thanks a lot. The misunderstanding is due to the font type not sure if it was x3 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?
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15 May 2016, 09:44
Senthil7 wrote: Bunuel thanks a lot. The misunderstanding is due to the font type not sure if it was x3 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? BunuelMathematically x  3/x can only mean x minus 3/x. If it were x3 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?
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05 Oct 2017, 10:13
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. Answer: D
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Re: If x^2 + 9/x^2 = 31, what is the value of x  3/x?
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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 = ±5We 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?
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13 Jun 2018, 08:09
dave13You can convert any a^2+b^2 to a^2+b^2 2ab+2ab=(ab)^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?
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13 Jun 2018, 12:25
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 = ±5We 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 dave13We 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 rearranging \((x  \frac{3}{x})^2 = x^2 + \frac{9}{x^2}  6 = 31  6 = 25\) [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?
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22 Mar 2019, 09:21
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.
x3/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?
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22 Mar 2019, 10:42
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 \((mn)^2 = m^2 + n^2  2mn\), 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?
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