Question

What is the square root of [2x + i {(x)^2 - 1}].please solve briefly .like
let √ ̅ [2x + i {(x)^2 - 1}] = a+ib

⇔ [2x + i {(x)^2 - 1}] = a^2 - b^2 +2iab

therefore 2x= a^2 - b^2

x^2 - 1 = 2ab

what will be next??? and i don t know (x^2 - 1)/2 either greater than 0 or less than 0 . if greater than 0 , then sign of a and b will be same , and if less than 0 , sign of a and b will be opposite . i m in a dilemma . therefore 4 answers will be possible??

i have found answers of the problem in two books different
in 1st book answer is ±(1/√2)[(x+1)+i(x-1)]
in 2nd book answer is ±(1/√2)[(x+1)+i(1-x)] which one is correct or both correct ?? then explain the reason