X^3> x^2 and |x| > 1, then
1. x > 1
2. x < -1
3. -1 < x < 1
4. x < -1 or x > 1
5. x < -1 and x > 1

1. X  > 1

Step-by-step explanation:

We know because . That's why

.

We can now subtract 1 in both sides of the inequality:

.

Factoring as a difference of cubes, we get:

.

Thus, we have two factors whose multiplication is positive. Then, both are positive or both are negative. The second case is impossible, because can never be positive. The reason is the following:

witch is always positive because is a sum of squares, and the squares are always positive.

We conclude that both and have to be positive, and then implies

why can't you?

step-by-step explanation: