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

Question

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

Karmesh · Accepted Answer

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

shridhar786 · Answer

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

QuantMadeEasy · Answer

(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

Archit3110 · Answer

#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

Ekland · Answer

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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dimri10 · Answer

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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Basshead · Answer

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.

DeeptiManyaExpert · Answer

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.

sacharya · Answer

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

JesWinters · Answer

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

Bunuel · Answer

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

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