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If a^3 + a^2 – a – 1 = 0, then which one of the following could be the

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If a^3 + a^2 – a – 1 = 0, then which one of the following could be the  [#permalink]

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New post Updated on: 04 Jan 2019, 09:10
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If a^3 + a^2 – a – 1 = 0, then which one of the following could be the value of a?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

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GOOD LUCK!


Originally posted by UB001 on 04 Jan 2019, 09:06.
Last edited by Bunuel on 04 Jan 2019, 09:10, edited 1 time in total.
Renamed the topic.
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Posts: 196
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If a^3 + a^2 – a – 1 = 0, then which one of the following could be the  [#permalink]

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New post Updated on: 04 Jan 2019, 11:02
1
Manipulating the question to give

\(a^3 + a^2 – a – 1 = 0\)
\(a^2(a + 1) – 1(a + 1) = 0\)
\((a^2 -1) (a + 1) = 0\)
\(a^2 = 1\) or a = -1

So as you can see there are no -ive values present in the answer options.

Correct answer will be B.
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Originally posted by KanishkM on 04 Jan 2019, 10:05.
Last edited by KanishkM on 04 Jan 2019, 11:02, edited 1 time in total.
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Re: If a^3 + a^2 – a – 1 = 0, then which one of the following could be the  [#permalink]

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New post 04 Jan 2019, 11:00
UB001 wrote:
If a^3 + a^2 – a – 1 = 0, then which one of the following could be the value of a?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

\({a^3} + {a^2} = a + 1\)

\(?\,\,\,:\,\,\,{\rm{could}}\,\,{\rm{be}}\,\,a\)

Let´s do a trivial alternatives INSPECTION:

\(\left( A \right)\,\,0\mathop = \limits^? 1\,\,\,{\rm{no}}\)

\(\left( B \right)\,\,2\mathop = \limits^? 2\,\,\,{\rm{yes}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{B}} \right)\)


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Fabio.
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Re: If a^3 + a^2 – a – 1 = 0, then which one of the following could be the &nbs [#permalink] 04 Jan 2019, 11:00
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