Solve u^2-1≥2 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for u

u \in (- \infty, - 3] \cup [3, + \infty)

Evaluate

u^{2} - 1 \geq 2

Move the expression to the left side

u^{2} - 1 - 2 \geq 0

Subtract the numbers

u^{2} - 3 \geq 0

Rewrite the expression

u^{2} - 3 = 0

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

u^{2} = 0 + 3

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

u^{2} = 3

Take the root of both sides of the equation and remember to use both positive and negative roots

u = \pm 3

Separate the equation into 2 possible cases

u = 3 u = - 3

Determine the test intervals using the critical values

u < - 3 - 3 < u < 3 u > 3

Choose a value form each interval

u_{1} = - 3 u_{2} = 0 u_{3} = 3

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

More Steps

u < - 3 is the solution u_{2} = 0 u_{3} = 3

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

More Steps

u < - 3 is the solution - 3 < u < 3 is not a solution u_{3} = 3

To determine if u > 3 is the solution to the inequality,test if the chosen value u = 3 satisfies the initial inequality

More Steps

u < - 3 is the solution - 3 < u < 3 is not a solution u > 3 is the solution

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

u \leq - 3 is the solution u \geq 3 is the solution

Solution

u \in (- \infty, - 3] \cup [3, + \infty)

Show Solution