Solve x^2-3|x^6|>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \frac{4 27}{3}, 0) \cup (0, \frac{4 27}{3})

Evaluate

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

When the expression in absolute value bars is not negative, remove the bars

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

Rewrite the expression

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

x = 0 x = \frac{4 27}{3} x = - \frac{4 27}{3}

Determine the test intervals using the critical values

x < - \frac{4 27}{3} - \frac{4 27}{3} < x < 0 0 < x < \frac{4 27}{3} x > \frac{4 27}{3}

Choose a value form each interval

x_{1} = - 2 x_{2} = - \frac{4 27}{6} x_{3} = \frac{4 27}{6} x_{4} = 2

To determine if x < - \frac{4 27}{3} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{4 27}{3} is not a solution x_{2} = - \frac{4 27}{6} x_{3} = \frac{4 27}{6} x_{4} = 2

To determine if - \frac{4 27}{3} < x < 0 is the solution to the inequality,test if the chosen value x = - \frac{4 27}{6} satisfies the initial inequality

More Steps

x < - \frac{4 27}{3} is not a solution - \frac{4 27}{3} < x < 0 is the solution x_{3} = \frac{4 27}{6} x_{4} = 2

To determine if 0 < x < \frac{4 27}{3} is the solution to the inequality,test if the chosen value x = \frac{4 27}{6} satisfies the initial inequality

More Steps

x < - \frac{4 27}{3} is not a solution - \frac{4 27}{3} < x < 0 is the solution 0 < x < \frac{4 27}{3} is the solution x_{4} = 2

To determine if x > \frac{4 27}{3} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{4 27}{3} is not a solution - \frac{4 27}{3} < x < 0 is the solution 0 < x < \frac{4 27}{3} is the solution x > \frac{4 27}{3} is not a solution

Solution

x \in (- \frac{4 27}{3}, 0) \cup (0, \frac{4 27}{3})

Show Solution