Solve x^2 x-1<0 - Socratic AI (ScanMath)

Evaluate

x^{2} \times x - 1 < 0

Multiply the terms

More Steps

x^{3} - 1 < 0

Rewrite the expression

x^{3} - 1 = 0

Move the constant to the right-hand side and change its sign

x^{3} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x^{3} = 1

Take the 3 -th root on both sides of the equation

3 x^{3} = 31

Calculate

x = 31

Simplify the root

x = 1

Determine the test intervals using the critical values

x < 1 x > 1

Choose a value form each interval

x_{1} = 0 x_{2} = 2

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

More Steps

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

Solution

x < 1

Alternative Form

x \in (- \infty, 1)

X^2 x 1<0