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(a^4 + 1)/a^2 =

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Joined: 02 Sep 2009
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(a^4 + 1)/a^2 =  [#permalink]

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New post 15 Nov 2019, 01:42
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:10) correct 35% (01:39) wrong based on 40 sessions

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\(\frac{a^4 + 1}{a^2}\) =


A. \((a+\frac{1}{a})(a-\frac{1}{a})\)

B. \((a+\frac{1}{a})^2\)

C. \((a + \frac{\sqrt{2}}{a})(a - \frac{\sqrt{2}}{a})\)

D. \((a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} - \frac{1}{a})\)

E. \((a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} + \frac{1}{a})\)


Are You Up For the Challenge: 700 Level Questions

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Re: (a^4 + 1)/a^2 =  [#permalink]

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New post 15 Nov 2019, 01:52
Bunuel wrote:
\(\frac{a^4 + 1}{a^2}\) =


A. \((a+\frac{1}{a})(a-\frac{1}{a})\)

B. \((a+\frac{1}{a})^2\)

C. \((a + \frac{\sqrt{2}}{a})(a - \frac{\sqrt{2}}{a})\)

D. \((a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} - \frac{1}{a})\)

E. \((a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} + \frac{1}{a})\)


\(\frac{a^4 + 1}{a^2}\)
--> \(a^2 + \frac{1}{a^2}\)
--> \(a^2 + \frac{1}{a^2} + 2*a*\frac{1}{a} - 2*a*\frac{1}{a}\)
--> \((a + \frac{1}{a})^2 - 2\)
--> \((a + \frac{1}{a})^2 - (\sqrt{2})^2\)
--> \((a + \frac{1}{a} + \sqrt{2})(a + \frac{1}{a} - \sqrt{2})\)

IMO Option E
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Re: (a^4 + 1)/a^2 =  [#permalink]

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New post 22 Nov 2019, 08:06
Bunuel wrote:
\(\frac{a^4 + 1}{a^2}\) =


A. \((a+\frac{1}{a})(a-\frac{1}{a})\)

B. \((a+\frac{1}{a})^2\)

C. \((a + \frac{\sqrt{2}}{a})(a - \frac{\sqrt{2}}{a})\)

D. \((a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} - \frac{1}{a})\)

E. \((a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} + \frac{1}{a})\)


Are You Up For the Challenge: 700 Level Questions

Plug a=1
Required value=2
Check options
E gives 2
E:)
GMAT Club Bot
Re: (a^4 + 1)/a^2 =   [#permalink] 22 Nov 2019, 08:06
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