If a=0 what is the number of solutions of equation x-a=square root(x^2-1).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation given is x - a = sqrt ( x^2 - 1) of which we have to find the number of solutions.

As a= 0

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

=> x = sqrt ( x^2 - 1)

square both the sides

x^2 = x^2 - 1

=> x^2 - x^2 = -1

=> 0 = -1 , which is not possible.

Therefore if a = 0, the equation x - a = sqrt ( x^2 - 1) has no solutions.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll impose the constraints of existence of the square root:

x^2 - 1 >=0

The expression x^2 - 1 is positive over the ranges (- infinite , -1] U [1 ; +infinite).

Now, we'll put a = 0 and we'll solve the given equation:

x = sqrt(x^2 - 1)

We'll raise to square both sides, in order to eliminate the square root:

x^2 = x^2 - 1

We'll subtract x^2:

x^2 - x^2 = -1

0 = -1 not true

The given equation has no solutions if a = 0.

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