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Posts: 3,651
Updated on: 17 Mar 2026, 21:05
Originally posted by EgmatQuantExpert on 27 Apr 2017, 22:09.
Last edited by Bunuel on 17 Mar 2026, 21:05, edited 5 times in total.
Last edited by Bunuel on 17 Mar 2026, 21:05, edited 5 times in total.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
64% (02:02) correct
36%
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wrong
based on 654
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If \(F(x + \frac{1}{x}) = x^2 + \frac{1}{x^2}\), what is the value of \(F(4) + F(5)\).
A. 9
B. 16
C. 25
D. 37
E. 41
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A. 9
B. 16
C. 25
D. 37
E. 41
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We know that the function
F(x+\(\frac{1}{x}\))=\(x^2 + \frac{1}{x^2}\)
To find F(4)
\(x + \frac{1}{x}\) = 4
Squaring on both sides
\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 16
\(x^2 + \frac{1}{x^2}\) = 16-2 =14
To find F(5)
\(x + \frac{1}{x}\) = 5
Squaring on both sides
\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 25
\(x^2 + \frac{1}{x^2}\) = 25-2 =23
So the sum of F(4) and F(5) = 14+23 = 37(Option D)
F(x+\(\frac{1}{x}\))=\(x^2 + \frac{1}{x^2}\)
To find F(4)
\(x + \frac{1}{x}\) = 4
Squaring on both sides
\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 16
\(x^2 + \frac{1}{x^2}\) = 16-2 =14
To find F(5)
\(x + \frac{1}{x}\) = 5
Squaring on both sides
\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 25
\(x^2 + \frac{1}{x^2}\) = 25-2 =23
So the sum of F(4) and F(5) = 14+23 = 37(Option D)
General Discussion
Posts: 3,651
Reserving this space to post the official solution. 
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keats
Joined: 28 Nov 2014
Last visit: 08 Jun 2019
Posts: 725
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Products:
Schools: Fisher '19 (M$)
Posts: 725
F(x + 1/x) = (x + 1/x)^2 - 2
So, the function can easily be reduced to F(y) = y^2 - 2 where y = x + 1/x
Therefore, F(4) + F(5) = (4^2-2) + (5^2-2) = 14 + 23 = 37
Pick D
So, the function can easily be reduced to F(y) = y^2 - 2 where y = x + 1/x
Therefore, F(4) + F(5) = (4^2-2) + (5^2-2) = 14 + 23 = 37
Pick D
Posts: 7
keats
Can someone please provide a better explanation?
Thanks in advance!
Posts: 7
pushpitkc
Could you please elaborate more on this part:
Squaring on both sides
\(x^2 + \frac{1}{x^2} + 2*x^2*\frac{1}{x^2}\) = 16
\(x^2 + \frac{1}{x^2}\) = 16-2 =14
It is not clear why and how you square both sides where digit 2 comes from?
Thank you very much!
\((a+b)^2 = a^2 + b^2 + 2*a*b\)
if a = x and b = 1/x
\((x+\frac{1}{x})^2 = x^2 + \frac{1}{x^2} + 2*x*\frac{1}{x}\)
Since x and \frac{1}{x} cancel out each other, we get 2.
if a = x and b = 1/x
\((x+\frac{1}{x})^2 = x^2 + \frac{1}{x^2} + 2*x*\frac{1}{x}\)
Since x and \frac{1}{x} cancel out each other, we get 2.
Posts: 7
pushpitkc
Thank you so much! Greatly appreciated!
EgmatQuantExpert
If we square \(x + \frac{1}{x}\) we will get \(x^2 + \frac{1}{x^2} + 2\).
So we can write \(F(x + \frac{1}{x})\) = \((x +\frac{1}{x})^2\) - 2 = \(x^2 + \frac{1}{x^2}\)
---> F(4) = (4)^2 - 2 = 14
and F(5) = (5)^2 - 2 = 23
Adding, 37.
sahilvijay
Joined: 29 Jun 2017
Last visit: 15 Apr 2021
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GPA: 4
WE:Engineering (Transportation)
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Posts: 288
Ans is D
f(x+ 1/x)= x^2 + 1/x^2 = ( x+1/x)^2-2
let x+1/x = y
f(y) = y^2-2
f(4)=16-2
f(5)=25-2
f(4)+f(5)=16+25-2-2=37
Option D
f(x+ 1/x)= x^2 + 1/x^2 = ( x+1/x)^2-2
let x+1/x = y
f(y) = y^2-2
f(4)=16-2
f(5)=25-2
f(4)+f(5)=16+25-2-2=37
Option D
sobby
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Joined: 14 Nov 2014
Last visit: 24 Jan 2022
Posts: 441
Location: India
Schools: Rotman '20 (S) Kelley '21 (S) (A)
GMAT 1: 700 Q50 V34
GPA: 3.76
F(x+1/X) = (x+1/x)^2 - 2
now put x+1/x = 4
F(4) = 16 - 2=14
same way F(5) = 23
total = 37
now put x+1/x = 4
F(4) = 16 - 2=14
same way F(5) = 23
total = 37
GMAT 1: 800 Q51 V51
Posts: 2,161
If \(F(x + \frac{1}{x}) = x^2 + \frac{1}{x^2}\), what is the value of \(F(4) + F(5)\)?
Looking at the information provided, we can recognize the following.
If we square \((x + \frac{1}{x})\), we get \((x + \frac{1}{x})^2 = x^2 + 2 + \frac{1}{x^2}\).
So, \(x^2 + \frac{1}{x^2} = (x + \frac{1}{x})^2 - 2\).
Thus, if \(F(x + \frac{1}{x}) = x^2 + \frac{1}{x^2}\), then \(F(x) = x^2 - 2\).
\(F(4) + F(5) = (4^2 - 2) + (5^2 - 2) = 14 + 23 = 37\)
A. 9
B. 16
C. 25
D. 37
E. 41
Correct answer: D
_________________
Looking at the information provided, we can recognize the following.
If we square \((x + \frac{1}{x})\), we get \((x + \frac{1}{x})^2 = x^2 + 2 + \frac{1}{x^2}\).
So, \(x^2 + \frac{1}{x^2} = (x + \frac{1}{x})^2 - 2\).
Thus, if \(F(x + \frac{1}{x}) = x^2 + \frac{1}{x^2}\), then \(F(x) = x^2 - 2\).
\(F(4) + F(5) = (4^2 - 2) + (5^2 - 2) = 14 + 23 = 37\)
A. 9
B. 16
C. 25
D. 37
E. 41
Correct answer: D
_________________
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