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

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Joined: 27 Dec 2012
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(a^4 + 1)/a^2 =  [#permalink]

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21 Nov 2014, 01:06
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:23) correct 33% (01:47) wrong based on 111 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: $$(a + \sqrt{2} + \frac{1}{a})(a - \sqrt{2} + \frac{1}{a})$$

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Joined: 30 Oct 2014
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GMAT 1: 670 Q48 V34
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Re: (a^4 + 1)/a^2 =  [#permalink]

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21 Nov 2014, 07:26
1

Method

A quick glance at the question and answer choices reveals that both are in the form of VARIABLES (Var).
The question requires us to equate L.H.S (Var) to R.H.S (Var). The best approach to solve such questions is to assume a value for the variable or variables.
Do keep in mind any specific conditions that the variables need to satisfy. (For example: In a question, if we are given that all the variable should be Distinct, Positive, Integers etc then we should only assume such values that satisfy these conditions).
In this question as no such condition is given. Assuming the value of variable a = 1. We can not assume variable to be equal to 0 as "a" is also available in the denominator.
Now if we put a=1 in the L.H.S. we get

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

Our answer will be the choice that gives 2 when we put a=1. Putting a=1 in each answer choice, we get:

A: 0

B: 4

C: -1

D: $$(2+\sqrt{2})(-\sqrt{2})$$

E: 2 (Our answer Choice)

To remember: We can visualize this approach as Var = Var and this question is a good example to practice its implementation.
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Re: (a^4 + 1)/a^2 =  [#permalink]

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21 Nov 2014, 10:09
I used similar to anujpoonia's solution. Will be curious to see how to simplify the expression though.
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(a^4 + 1)/a^2 =  [#permalink]

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23 Nov 2014, 18:44
2
Krage17 wrote:
I used similar to anujpoonia's solution. Will be curious to see how to simplify the expression though.

$$\frac{a^4 + 1}{a^2} = a^2 + \frac{1}{a^2} = a^2 + 2 + \frac{1}{a^2} - 2$$

$$= (a + \frac{1}{a})^2 - (\sqrt{2})^2$$

$$= (a + \frac{1}{a} + \sqrt{2}) (a + \frac{1}{a} - \sqrt{2})$$

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Re: (a^4 + 1)/a^2 =  [#permalink]

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04 Aug 2018, 06:10
Hello from the GMAT Club BumpBot!

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Re: (a^4 + 1)/a^2 =   [#permalink] 04 Aug 2018, 06:10
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