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# IF F(x + 1/x) = x^2 + 1/x^2....what is the value of

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IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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27 Apr 2017, 22:09
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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

Thanks,
Saquib
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[Reveal] Spoiler: OA

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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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27 Apr 2017, 22:10
Reserving this space to post the official solution.
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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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27 Apr 2017, 22:41
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

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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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21 May 2017, 01:07
keats wrote:
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

Can someone please provide a better explanation?

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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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21 May 2017, 01:33
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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)
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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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21 May 2017, 02:02
pushpitkc wrote:
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)

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!

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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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21 May 2017, 02:12
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$$(a+b)^2 = a^2 + b^2 + 2*a*b$$
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.
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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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21 May 2017, 05:50
pushpitkc wrote:
$$(a+b)^2 = a^2 + b^2 + 2*a*b$$
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.

Thank you so much! Greatly appreciated!

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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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30 Jun 2017, 05:54
EgmatQuantExpert wrote:
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

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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
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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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01 Sep 2017, 13:17
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
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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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01 Sep 2017, 23:40
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

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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of   [#permalink] 01 Sep 2017, 23:40
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