x^n = x^(n+2)

[navalpike]

I’ve seen this in another link but the explanation did not help.

x^n = x^(n+2) for any integer n. Is it true that x>0?

1. x=(x^2) – 2
2. 2x < x^5

Kindly show your thought process. Thanks.

[vamsikrishnach]

Heey..the given eqn can be simplified to x=+1 or -1.

Coming to option 1,you can simplify it to x(x-1)=2 and only -1 or 2 satisifie this eqn. So with this we can say x = -1. So question is answered that x is < 0.

Option 2 does not give integer values for x so ,IMO ans is A

[ssmiles08]

I’ve seen this in another link but the explanation did not help.

x^n = x^(n+2) for any integer n. Is it true that x>0?

1. x=(x^2) – 2
2. 2x < x^5

Kindly show your thought process. Thanks.

the question stem further simplified:

x^(n+2) - x^n = 0.

x^n(x^2 - 1) = 0

(x^2 - 1) = (x-1)(x+1)

so it can be written as x^n(x+1)(x-1) = 0.

1)
x^2 - x - 2 = 0

(x-2)(x+1) = 0

from here we can conclude that x = -1 given the help of the question stem. SUFF.

2) x can be various values depending on n. x = -1, 2, n can be 0, 2...so on INSUFF.

IMO A.

[navalpike]

1)
x^2 - x - 2 = 0

(x-2)(x+1) = 0

from here we can conclude that x = -1 given the help of the question stem. SUFF.

But can we also not conlude that x = 2?

[ssmiles08]

But can we also not conlude that x = 2?

No because in the question stem it tells you that x must +1 or -1 or 0.

(x^2 - 1) = (x-1)(x+1)

for x^n = 0, x= 0.


when statement 1 tells us that x = 2 or x = -1, we can take out 2 b/c it tells you x can only be -1, 1 or 0.

in this case, we can confirm x = -1.

[kaulnikhil]

Doesnt the second ans also help us to reach the conclusion that X=-1
all other values which we get for second dont match with x=1 or x=0
which we have obtained from the question ..hence according to me second also is sufficient ..
Am i on the right track ??

[hk]

I would go with D

the question can be simplified as X= -1 , 0, 1

And then main question is => is x>0?

1) Substitute value of x as -1, 1, 0 and you will find out that only x=-1 solves the equation. => Sufficient
2) Similarly substitute the same values of x and you will find that only x=-1 will solve the inequality!!! => Sufficient!!