Solve x ^ 4 < x ^ 2

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

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

Evaluate

x^{4} < x^{2}

Move the expression to the left side

x^{4} - x^{2} < 0

Rewrite the expression

x^{4} - x^{2} = 0

Factor the expression

x^{2} (x^{2} - 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 1 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x^{2} - 1 = 0

Solve the equation

More Steps

x = 0 x = 1 x = - 1

Determine the test intervals using the critical values

x < - 1 - 1 < x < 0 0 < x < 1 x > 1

Choose a value form each interval

x_{1} = - 2 x_{2} = - \frac{1}{2} x_{3} = \frac{1}{2} x_{4} = 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 < - 1 is not a solution x_{2} = - \frac{1}{2} x_{3} = \frac{1}{2} x_{4} = 2

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

More Steps

x < - 1 is not a solution - 1 < x < 0 is the solution x_{3} = \frac{1}{2} x_{4} = 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 < - 1 is not a solution - 1 < x < 0 is the solution 0 < x < 1 is the solution x_{4} = 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 < - 1 is not a solution - 1 < x < 0 is the solution 0 < x < 1 is the solution x > 1 is not a solution

Solution

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

Show Solution