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

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We need to know the number of solutions of x - a = sqrt(x^2 - 1) if a = 0.

x = sqrt(x^2 - 1)

=> x^2 = x^2 - 1

=> x^2 - x^2 = 1

=> 0 = 1

which is impossible.

Therefore there are no solutions.

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