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What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3

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gmatt1476
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What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   21 Sep 2019, 16:35
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What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01
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A
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   30 Sep 2019, 08:34
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gmatt1476
What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01

You actually don't need to solve this one. JUST THINK.

1. Take the denominator to the other side and we have ( x^4 + x^2 + 1 )^2 =1
When will LHS be equal to 1? before looking any further just give it a thought.
.
x^4 and x^2 are both +ve, so the only case possible is when x=0.
S1 SUFF

2. x^3 can be -ve, so apart from 0 you can also have x=-1. This gives us 2 values.
INSUFF

A
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   22 Sep 2019, 21:05
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STATEMENT (1)--\(x^4+x^2+1\) = \(\frac{1}{x^4+x^2+1}\)
let \(x^4+x^2+1\) = t
\(t^2\) = 1
(t+1)(t-1) = 0
t cant be -1 (\(x^4+x^2+1\) = +ve)
so t = 1
\(x^4+x^2+1\) = 1
\(x^2(x^2+1)\) = 0
x = 0
SUFFICIENT

STATEMENT (2)--\(x^3+x^2\) = 0
\(x^2(x+1)\) = 0
x can be 0, -1
INSUFFICIENT

A is the answer
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   22 Sep 2019, 22:48
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gmatt1476
What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01

(1) Simplifying the expression we get (x^2+1)^2 = 1
(x^2+1) = =/-1
x^2 = 0 or x^2 = -1(not possible)

Sufficient

(2) x^2(x+1)=0
x=0 or -1. No sufficient

A is correct
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   13 Jun 2020, 10:57
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gmatt1476
What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01


#1
\(x^4 + x^2 + 1 =\frac{1}{x^4 + x^2 + 1}\)
or say (x^4 + x^2 + 1)^2 = 1
so x has to be 0
sufficient
#2
\(x^3 + x^2 = 0\)
x can be -1 or 0
insufficient
OPTION A
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   13 Jun 2020, 13:29
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Statement 2 gives us 2 solution
Statement 1 in fact states that X=1/X
The only number that is equal to its reciprocal is |1|, means: -1 or 1.
The long term x^4+x^2+1 must be positive so in order to make 1=1 , X must be 0. Only one value is sufficient

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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   12 Nov 2020, 17:05
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What is the value of x?

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

\((x^4 + x^2 + 1)^2 = 1\)

The only way the above = 1 is if x = 0. SUFFICIENT.

(2) \(x^3 + x^2 = 0\)

x\(^2(x+1) = 0\)
\(x = 0\) or \(x = -1\). INSUFFICIENT.

Answer is A.
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   27 Jan 2023, 02:42
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yogendraaaa
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gmatt1476
What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01

You actually don't need to solve this one. JUST THINK.

1. Take the denominator to the other side and we have ( x^4 + x^2 + 1 )^2 =1
When will LHS be equal to 1? before looking any further just give it a thought.
.
x^4 and x^2 are both +ve, so the only case possible is when x=0.
S1 SUFF

2. x^3 can be -ve, so apart from 0 you can also have x=-1. This gives us 2 values.
INSUFF

A


But the question doesn't specify that X is a real number? Is it safe to assumer that GMAT sums only concern real numbers?

On the GMAT all numbers used are real numbers by default.
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What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   Updated on: 17 Jun 2020, 12:19
gmatt1476
What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01

Squaring a number can NEVER give you negative value or zero.

U can only get zero if and only if the number you're squaring is zero itself.

A


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Give a kudos for Gmatclub's sake

Originally posted by Ekland on 13 Jun 2020, 13:14.
Last edited by Ekland on 17 Jun 2020, 12:19, edited 2 times in total.
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   29 Jan 2021, 05:43
Question is to find value of x.

(1) Be careful with the Rational equations. Make sure that the denominator should not become zero with the value you get for x. Simplify the expression to get \((x^4 + x^2+1)^2 = 1\)
\((x^4 + x^2 + 1) = ±1\)
Since \(x^4 \)and\( x^2\) are positive, RHS cannot be negative.
Think of the values for x which can make the statement true.
x = 0
Sufficient

(2) x\(^2(x + 1) = 0\)
=> x = 0 or -1
Not sufficient

Thus, the answer is A.

Hope this helps. :)
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   29 Mar 2022, 20:25
Stmt 1:
\((x^{4} + x^{2} + 1)^{2}\)=1

\((x^{4} + x^{2} + 1) = 1\) ---> (1) OR
\((x^{4} + x^{2} + 1) = -1\) ----> (2)

Solving (1) \((x^{4} + x^{2} + 1) = 1\)

\((x^{4} + x^{2})=0\)

\(x^{2}(x^{2}+1)=0\)
Therefore, x=0

Considering 2 , \((x^{4} + x^{2} + 1) = -1\) --> Not possible since \(x^{4}\) , \(x^{2}\) and 1 are all positive
Hence, stmt 1 sufficient

Stmt 2:
\(x^{3}+x^{2}=0\)
\(x^{2}(x+1)=0\)
x=0 or x=-1 , 2 solutions
Not sufficient

Ans. A
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   27 Jan 2023, 01:20
Karmesh
gmatt1476
What is the value of x?


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

(2) \(x^3 + x^2 = 0\)



DS64402.01

You actually don't need to solve this one. JUST THINK.

1. Take the denominator to the other side and we have ( x^4 + x^2 + 1 )^2 =1
When will LHS be equal to 1? before looking any further just give it a thought.
.
x^4 and x^2 are both +ve, so the only case possible is when x=0.
S1 SUFF

2. x^3 can be -ve, so apart from 0 you can also have x=-1. This gives us 2 values.
INSUFF

A


But the question doesn't specify that X is a real number? Is it safe to assumer that GMAT sums only concern real numbers?
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink] What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3   14 Mar 2024, 19:35
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Re: What is the value of x? (1) x^4 + x^2 + 1 =1/(x^4 + x^2 + 1) (2) x^3 [#permalink]
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