Solve k^2-4<1 - ScanMath

Evaluate

k^{2} - 4 < 1

Move the expression to the left side

k^{2} - 4 - 1 < 0

Subtract the numbers

k^{2} - 5 < 0

Rewrite the expression

k^{2} - 5 = 0

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

k^{2} = 0 + 5

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

k^{2} = 5

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

k = \pm 5

Separate the equation into 2 possible cases

k = 5 k = - 5

Determine the test intervals using the critical values

k < - 5 - 5 < k < 5 k > 5

Choose a value form each interval

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

To determine if k < - 5 is the solution to the inequality,test if the chosen value k = - 3 satisfies the initial inequality

More Steps

k < - 5 is not a solution k_{2} = 0 k_{3} = 3

To determine if - 5 < k < 5 is the solution to the inequality,test if the chosen value k = 0 satisfies the initial inequality

More Steps

k < - 5 is not a solution - 5 < k < 5 is the solution k_{3} = 3

To determine if k > 5 is the solution to the inequality,test if the chosen value k = 3 satisfies the initial inequality

More Steps

k < - 5 is not a solution - 5 < k < 5 is the solution k > 5 is not a solution

Solution

- 5 < k < 5

Alternative Form

k \in (- 5, 5)

Solve the inequality