We have to solve sqrt(x^2 - 5) - sqrt(x^2 - 8) = 1

sqrt(x^2 - 5) - sqrt(x^2 - 8) = 1

square both the sides

x^2 - 5 + x^2 - 8 - 2* sqrt [(x^2 - 5)(x^2 - 8)] = 1

=> 2x^2 - 14 - 2* sqrt...

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We have to solve sqrt(x^2 - 5) - sqrt(x^2 - 8) = 1

sqrt(x^2 - 5) - sqrt(x^2 - 8) = 1

square both the sides

x^2 - 5 + x^2 - 8 - 2* sqrt [(x^2 - 5)(x^2 - 8)] = 1

=> 2x^2 - 14 - 2* sqrt [(x^2 - 5)(x^2 - 8)] = 0

=> x^2 - 7 = sqrt [(x^2 - 5)(x^2 - 8)]

square both the sides

=> x^4 + 49 - 14x^2 = x^4 - 13x^2 + 40

=> 9 - x^2 = 0

=> x^2 = 9

=> x = 3 and x = -3

**The required solutions are x = 3 and x = -3**