If n is an integer and x^n - x^-n = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠0
the way that i approached this problem is:
n=0, n=1, n=-1 all satisfy the equation above, i.e. with each of those values of n, you get result zero
statement 1) x is an integer.
x=1, satisfies eqt when n=0
x=-1, satisfies eqt when n=0
since we can have two values of x, insuff.
statement 2) n cannot be zero
n can still be 1 or -1
if we take n=1, then we can simplify the expression to x=1/x
which gives us x^2=1, and that results in 2 values of x, specifically x=1, x=-1
thus insuff
statement 1 + statement 2)
n cannot be zero and x must be an integer
taking the same example that i used for statement 2, it can be proven that you get two values for x
thus this is also insufficient
thus answer E
(1) x is an integer.
(2) n ≠0
the way that i approached this problem is:
n=0, n=1, n=-1 all satisfy the equation above, i.e. with each of those values of n, you get result zero
statement 1) x is an integer.
x=1, satisfies eqt when n=0
x=-1, satisfies eqt when n=0
since we can have two values of x, insuff.
statement 2) n cannot be zero
n can still be 1 or -1
if we take n=1, then we can simplify the expression to x=1/x
which gives us x^2=1, and that results in 2 values of x, specifically x=1, x=-1
thus insuff
statement 1 + statement 2)
n cannot be zero and x must be an integer
taking the same example that i used for statement 2, it can be proven that you get two values for x
thus this is also insufficient
thus answer E
