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What is the value of x? (1) x^4+x^2+1=(1/x^4+x^2+1) (2)

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What is the value of x? (1) x^4+x^2+1=(1/x^4+x^2+1) (2) [#permalink] New post 15 May 2007, 18:48
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0

What is the greatest integer n such that 13/n is an integer for all consecutive even integers r and s?
A. 10
B. 8
C. 6
D. 4
E. 2
Manager
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 [#permalink] New post 15 May 2007, 19:12
both the que are not clear to me...
james
in first que
(1) x^4+x^2+1=(1/x^4+x^2+1) or x^4+x^2+1=1/(x^4+x^2+1)
(2) x3+x^2=0 or x^3+x^2=0

second que also i am clueless...help
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Re: prep questions [#permalink] New post 15 May 2007, 19:17
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0


i did not get 1 but 2 is sufficient.

x = -1.


second question: no idea what is the question is about?

Last edited by Himalayan on 15 May 2007, 19:19, edited 1 time in total.
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Re: prep questions [#permalink] New post 15 May 2007, 19:18
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0



(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)
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Re: prep questions [#permalink] New post 15 May 2007, 21:42
kirakira wrote:
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0



(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)


you are correct in statement 2 but st 1 is also insufficient cuz:

=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = -1 or 1.

from 1 and 2, x should be 0.
seems C.
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 [#permalink] New post 15 May 2007, 21:56
In GMAT,

(x^2)^(1/2) = +x and not -x

as in -

9^(1/2) is always taken as +3

However, when we have a situation x^2 = 9, then we have to take into consideration of x = 3 and x = -3 !

Can also see the same in OG 11TH edition P-126 under Modulus

"note that (x^2)^(1/2) denotes the non-negative square root of x^2"

So if we consider the above, answer A :)
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Re: prep questions [#permalink] New post 15 May 2007, 23:17
Himalayan wrote:
kirakira wrote:
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0



(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)


you are correct in statement 2 but st 1 is also insufficient cuz:

=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = -1 or 1.

from 1 and 2, x should be 0.
seems C.


(x^4 + x^2 + 1) is always positive.
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 [#permalink] New post 16 May 2007, 06:32
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x^3+x^2=0

the answer is supposed to be A
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Re: prep questions [#permalink] New post 16 May 2007, 08:07
kirakira wrote:
Himalayan wrote:
kirakira wrote:
Jamesk486 wrote:
What is the value of x?
(1) x^4+x^2+1=(1/x^4+x^2+1)
(2) x3+x^2=0



(A) it is

(1) x^4+x^2+1=(1/x^4+x^2+1)
=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = 1
=> x^4 + x^2 = 0
=> x^2(x^2 + 1) = 0
=> x = 0 => suff

(2) x^3 + x^2 = x^2(x + 1) = 0
=> x = 0 or x = -1 => insuff

Hence, (A)


you are correct in statement 2 but st 1 is also insufficient cuz:

=> (x^4+x^2+1)^2 = 1
=> x^4 + x^2 + 1 = -1 or 1.

from 1 and 2, x should be 0.
seems C.


(x^4 + x^2 + 1) is always positive.


good point and you r right. 8-)
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 [#permalink] New post 16 May 2007, 09:37
for qstn 1 1. is x^8 = 1 and 2. leads to x = 0 or x = -1. ==> x = -1
So answer C
  [#permalink] 16 May 2007, 09:37
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