Question

Find the roots of x square - 2 x minus a square minus one

Answer 1

Given: The equation  x square - 2 x minus a square minus one

To find: The roots of the given equation.

Solution:

• Now we have given the equation as:

                x^2 - 2x - (a^2 - 1) = 0

• The roots will be:

                -b ± √(b^2 - 4(ac)) / 2a

• So applying this formula, we get:

                -(-2) ± √((-2)^2 - 4(1)(a^2 - 1)) / 2

• Now simplifying this, we get:

                2 ± √( 4 - 4a^2 + 4 ) / 2

                2 ± √( 8 - 4a^2 ) / 2

                2 ± √4( 2 - a^2 ) / 2

                2 ± 2√( 2 - a^2 ) / 2

• Cancelling 2, we get:

                1 ± √( 2 - a^2 )

Answer:

          So the roots of the given equation is 1 ± √( 2 - a^2 ) .