Solve a^2>1 - ScanMath

Evaluate

a^{2} > 1

Move the expression to the left side

a^{2} - 1 > 0

Rewrite the expression

a^{2} - 1 = 0

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

a^{2} = 0 + 1

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

a^{2} = 1

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

a = \pm 1

Simplify the expression

a = \pm 1

Separate the equation into 2 possible cases

a = 1 a = - 1

Determine the test intervals using the critical values

a < - 1 - 1 < a < 1 a > 1

Choose a value form each interval

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

To determine if a < - 1 is the solution to the inequality,test if the chosen value a = - 2 satisfies the initial inequality

More Steps

a < - 1 is the solution a_{2} = 0 a_{3} = 2

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

More Steps

a < - 1 is the solution - 1 < a < 1 is not a solution a_{3} = 2

To determine if a > 1 is the solution to the inequality,test if the chosen value a = 2 satisfies the initial inequality

More Steps

a < - 1 is the solution - 1 < a < 1 is not a solution a > 1 is the solution

Solution

a \in (- \infty, - 1) \cup (1, + \infty)

Solve the inequality