Solve sqrt(x^2-1)

Evaluate

x^{2} - 1

To find the roots of the expression,set the expression equal to 0

x^{2} - 1 = 0

Find the domain

More Steps

x^{2} - 1 = 0, x \in (- \infty, - 1] \cup [1, + \infty)

Calculate

x^{2} - 1 = 0

The only way a root could be 0 is when the radicand equals 0

x^{2} - 1 = 0

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

x^{2} = 0 + 1

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

x^{2} = 1

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

x = \pm 1

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

Check if the solution is in the defined range

x = 1 x = - 1, x \in (- \infty, - 1] \cup [1, + \infty)

Find the intersection of the solution and the defined range

x = 1 x = - 1

Solution

x_{1} = - 1, x_{2} = 1

Find the roots