SOLUTION: If a^(1/2)-a^(-1/2)=1, show that a+a^-1=3

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Question 1177485: If a^(1/2)-a^(-1/2)=1, show that a+a^-1=3
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Start from


    a^(1/2) - a^(-1/2) = 1.



Square both sides.   You will get


    a - 2 + a^(-1) = 1


    a + a^(-1) = 1 + 2 = 3,


which is what has to be proved.

At this point, the solution is completed.