Solve x^3 x^2 - 26x^24 ≥ 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in [2313, + \infty) \cup {0}

Evaluate

x^{3} \times x^{2} - 26 x^{2} \times 4 \geq 0

Simplify

More Steps

x^{5} - 104 x^{2} \geq 0

Rewrite the expression

x^{5} - 104 x^{2} = 0

Factor the expression

x^{2} (x^{3} - 104) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{3} - 104 = 0

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

x = 0 x^{3} - 104 = 0

Solve the equation

More Steps

x = 0 x = 2313

Determine the test intervals using the critical values

x < 0 0 < x < 2313 x > 2313

Choose a value form each interval

x_{1} = - 1 x_{2} = 2 x_{3} = 6

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 not a solution x_{2} = 2 x_{3} = 6

To determine if 0 < x < 2313 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 2313 is not a solution x_{3} = 6

To determine if x > 2313 is the solution to the inequality,test if the chosen value x = 6 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 2313 is not a solution x > 2313 is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \geq 2313 is the solution x = 0

Solution

x \in [2313, + \infty) \cup {0}

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