x^3-x > 0
-1 < x < 0
x > 1
Insufficient as we do not know which range x falls into.
2) x^2 > x > 0
- We know x must be positive
- We know x^2 must be greater than x, so x cannot be a positive fraction (e.g. 1/2)
- We know x cannot be 1 as well since this will result in x^2 = x
Wilfred & girish,
I got how you treated first condition but I have a different view here.
x^3 > x
Without solving it, if we plug & play in this equation, we easily get the range of x i.e. x>1
1) For x < 0
x^3 < x, if x = -3, x^3 = -27
2) For 0 < x < 1
x^3 < x, if x = 0.2, x^3 = 0.008
3) For x > 1
x^3 > x, if x = 3, x^3 = 27
The only range that satisfies x^3 > x, is x > 1.
Am I missing something?