Solve x^4 -1 > x 1

Evaluate

x^{4} - 1 > x \times 1

Any expression multiplied by 1 remains the same

x^{4} - 1 > x

Move the expression to the left side

x^{4} - 1 - x > 0

Rewrite the expression

x^{4} - 1 - x = 0

Find the critical values by solving the corresponding equation

x \approx 1.220744 x \approx - 0.724492

Determine the test intervals using the critical values

x < - 0.724492 - 0.724492 < x < 1.220744 x > 1.220744

Choose a value form each interval

x_{1} = - 2 x_{2} = 0 x_{3} = 2

To determine if x < - 0.724492 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 0.724492 is the solution x_{2} = 0 x_{3} = 2

To determine if - 0.724492 < x < 1.220744 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 0.724492 is the solution - 0.724492 < x < 1.220744 is not a solution x_{3} = 2

To determine if x > 1.220744 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 0.724492 is the solution - 0.724492 < x < 1.220744 is not a solution x > 1.220744 is the solution

Solution

x \in (- \infty, - 0.724492) \cup (1.220744, + \infty)

Solve the inequality