If n is an integer and x^n - x-^n =0.What is the value of x?
1) x is an integer
2)n is not equal to 0.
Value of x
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x^n - x^-n = 0
The domain of x here is R-{0}. now if x= 1, it satisfies the equation.
x= -1 also satisfies the equation so the first statement doesn give any single value. moreover if n is zero, then again the equation gets satisfied.
The second statement says n is not zero, then this gives us x=+/-1,
combining the above two will also not give us a single value which is either 1 or -1. so the ans is cant be determined.
The domain of x here is R-{0}. now if x= 1, it satisfies the equation.
x= -1 also satisfies the equation so the first statement doesn give any single value. moreover if n is zero, then again the equation gets satisfied.
The second statement says n is not zero, then this gives us x=+/-1,
combining the above two will also not give us a single value which is either 1 or -1. so the ans is cant be determined.
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I am assuming that the question is actually x^n-x^(-n)=0. Which can be further resolved to x^n - 1/(x^n) = 0 ==> x^(2n) - 1 = 0 ==> x^(2n) = 1.
Stmt 1: This statement is saying that x is an integer. Well, it can be any integer as long as n is 0 (remember o is an even integer). The above equation can be written as x^(2n) = x^0. Hence this statement is not sufficient.
Stmt 2: This statement says that n is not equal to 0. In this case, x can equal to 1 or -1. This statement is not sufficient.
Both the statements together will also not give us the value of x.
Hence, answer should be E
Stmt 1: This statement is saying that x is an integer. Well, it can be any integer as long as n is 0 (remember o is an even integer). The above equation can be written as x^(2n) = x^0. Hence this statement is not sufficient.
Stmt 2: This statement says that n is not equal to 0. In this case, x can equal to 1 or -1. This statement is not sufficient.
Both the statements together will also not give us the value of x.
Hence, answer should be E
Last edited by Vemuri on Sun Apr 26, 2009 5:12 pm, edited 1 time in total.
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I am assuming the question is
x^n - x^( - n) = 0
Rephrase x^n = x^ (-n)
x^n = 1/ x^n
Stmt I
x is an integer
x=2 n=0
x=1 n=0
INSUFF
Stmt II
n is not 0
x=1 n=2
x= -1 n=2
INSUFF
Together:
x can still be 1 or -1
ISNUFF
Choose E
x^n - x^( - n) = 0
Rephrase x^n = x^ (-n)
x^n = 1/ x^n
Stmt I
x is an integer
x=2 n=0
x=1 n=0
INSUFF
Stmt II
n is not 0
x=1 n=2
x= -1 n=2
INSUFF
Together:
x can still be 1 or -1
ISNUFF
Choose E
- cubicle_bound_misfit
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basically,
the q can be simplified as x^2n =1
for no fractional x which is possible.
but possible for +/- 1 hence E.
the q can be simplified as x^2n =1
for no fractional x which is possible.
but possible for +/- 1 hence E.
Cubicle Bound Misfit
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Thanks everyone.OA is E.cramya wrote:I am assuming the question is
x^n - x^( - n) = 0
Rephrase x^n = x^ (-n)
x^n = 1/ x^n
Stmt I
x is an integer
x=2 n=0
x=1 n=0
INSUFF
Stmt II
n is not 0
x=1 n=2
x= -1 n=2
INSUFF
Together:
x can still be 1 or -1
ISNUFF
Choose E
And the question was properly written by you.
Trust but verify.