SOLUTION: Solve: (x^2 - 1)^1/2 + (x^2 - 1)^-1/2 = 2 Any help would be very much appreciated. Thank you

Algebra ->  Rational-functions -> SOLUTION: Solve: (x^2 - 1)^1/2 + (x^2 - 1)^-1/2 = 2 Any help would be very much appreciated. Thank you      Log On


   

Question 446023: Solve:
(x^2 - 1)^1/2 + (x^2 - 1)^-1/2 = 2
Any help would be very much appreciated.
Thank you
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-1%29%5E%281%2F2%29%2B1%2F%28x%5E2-1%29%5E%281%2F2%29=5%2F2,multiply both sides by %28x%5E2-1%29%5E%281%2F2%29
%28x%5E2-1%29%2B1=%285%2F2%29%28x%5E2-1%29%5E%281%2F2%29=>x%5E2=%285%2F2%29%28x%5E2-1%29%5E%281%2F2%29. Raise to the
second power both sides of equation:x%5E4=%2825%2F4%29%28x%5E2-1%29, set the equation to
zero:4x%5E4-25x%5E2%2B25=0, substitute x%5E2=y and get a quadratic equation:
4y%5E2-25y%2B25=0, solving this equation we find:y=5 and y=5/4.
Knowing that, x%5E2=5, get x=sqrt%285%29 and x=-sqrt%285%29
Also from x%5E2=5%2F4, we get x=sqrt%28%285%29%2F2%29 and x=-sqrt%28%285%29%2F2%29
Thus, the solution set is:[ sqrt%285%29, -sqrt%285%29, sqrt%285%29%2F2,
-sqrt%285%29%2F2]