Solve (x^4-6x^2 8>0)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, - 43) \cup (43, + \infty)

Evaluate

x^{4} - 6 x^{2} \times 8 > 0

Multiply the terms

x^{4} - 48 x^{2} > 0

Rewrite the expression

x^{4} - 48 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 48) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 48 = 0

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

x = 0 x^{2} - 48 = 0

Solve the equation

More Steps

x = 0 x = 43 x = - 43

Determine the test intervals using the critical values

x < - 43 - 43 < x < 0 0 < x < 43 x > 43

Choose a value form each interval

x_{1} = - 8 x_{2} = - 3 x_{3} = 3 x_{4} = 8

To determine if x < - 43 is the solution to the inequality,test if the chosen value x = - 8 satisfies the initial inequality

More Steps

x < - 43 is the solution x_{2} = - 3 x_{3} = 3 x_{4} = 8

To determine if - 43 < x < 0 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 43 is the solution - 43 < x < 0 is not a solution x_{3} = 3 x_{4} = 8

To determine if 0 < x < 43 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 43 is the solution - 43 < x < 0 is not a solution 0 < x < 43 is not a solution x_{4} = 8

To determine if x > 43 is the solution to the inequality,test if the chosen value x = 8 satisfies the initial inequality

More Steps

x < - 43 is the solution - 43 < x < 0 is not a solution 0 < x < 43 is not a solution x > 43 is the solution

Solution

x \in (- \infty, - 43) \cup (43, + \infty)

Show Solution