SOLUTION: Kindly help me solving it If {{{a=3+2sqrt2}}} then the value of {{{a^(1/2)+a^(-1/2)}}} is?

Algebra ->  Exponents -> SOLUTION: Kindly help me solving it If {{{a=3+2sqrt2}}} then the value of {{{a^(1/2)+a^(-1/2)}}} is?      Log On


   

Question 1045796: Kindly help me solving it
If a=3%2B2sqrt2 then the value of a%5E%281%2F2%29%2Ba%5E%28-1%2F2%29 is?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let a=3%2B2sqrt%282%29.
Now %28a%5E%281%2F2%29+%2B+a%5E%28-1%2F2%29%29%5E2+=+a+%2B+2+%2B+a%5E%28-1%29
Since %283%2B2sqrt%282%29%29%283-2sqrt%282%29%29+=+1, then a%5E%28-1%29+=+1%2Fa+=+3+-2sqrt%282%29.

===> .

Because a%5E%281%2F2%29+%2B+a%5E%28-1%2F2%29+%3E+0, we then get
a%5E%281%2F2%29+%2B+a%5E%28-1%2F2%29+=+2sqrt%282%29,
after taking square roots of both sides.