Solve 3x^6-x>2x^2

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, 0) \cup (1, + \infty)

Evaluate

3 x^{6} - x > 2 x^{2}

Move the expression to the left side

3 x^{6} - x - 2 x^{2} > 0

Rewrite the expression

3 x^{6} - x - 2 x^{2} = 0

Factor the expression

x (x - 1) (3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 1) = 0

Separate the equation into 3 possible cases

x = 0 x - 1 = 0 3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 1 = 0

Solve the equation

More Steps

x = 0 x = 1 3 x^{4} + 3 x^{3} + 3 x^{2} + 3 x + 1 = 0

Solve the equation

x = 0 x = 1 x \in / R

Find the union

x = 0 x = 1

Determine the test intervals using the critical values

x < 0 0 < x < 1 x > 1

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{1}{2} x_{3} = 2

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is the solution x_{2} = \frac{1}{2} x_{3} = 2

To determine if 0 < x < 1 is the solution to the inequality,test if the chosen value x = \frac{1}{2} satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 1 is not a solution x_{3} = 2

To determine if x > 1 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 1 is not a solution x > 1 is the solution

Solution

x \in (- \infty, 0) \cup (1, + \infty)

Show Solution