# How do you solve #x^3-2x>1#?

##### 1 Answer

#### Explanation:

The simplest method is graphing the function f(x), then looking for the parts of the graph that are above the x-axis.

graph{x^3 - 2x - 1 [-2.5, 2.5, -1.25, 1.25]}

On this graph, the x-intercepts are approximately:

x = - 1 , x = - 0.65, and x = 1.60

Answers by intervals:

(-1, - 0.65) and (1.60, + inf.)

**Note 1** . We can find the exact values of the 3 x-intercepts by solving the equation

f(x) = x^3 - 2x - 1 = (x + 1)(x^2 - x - 1) = 0

The quadratic equation (x^2 - x - 1) = 0 gives 2 real roots:

x = (1 +- sqrt5)/2.

Therefor, the answers are:

**Note 2** . Graphing calculator may give much more accurate values of the three x-intercepts.

Note 3. Another method is solving algebraically the inequality by creating a Sign Chart. See algebra books.