SOLUTION: If x^(1/4) + x^(-1/4) = sqr2 + 1, find the value of x^(1/2) + x^(-1/2) and x + x^(-1), leaving your answers in surd form. Where do I begin? Thanks!

Algebra ->  Expressions -> SOLUTION: If x^(1/4) + x^(-1/4) = sqr2 + 1, find the value of x^(1/2) + x^(-1/2) and x + x^(-1), leaving your answers in surd form. Where do I begin? Thanks!      Log On


   

Question 1057683: If x^(1/4) + x^(-1/4) = sqr2 + 1, find the value of x^(1/2) + x^(-1/2) and x + x^(-1), leaving your answers in surd form.
Where do I begin? Thanks!
Answer by ikleyn(52833) About Me  (Show Source):
You can put this solution on YOUR website!
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If x^(1/4) + x^(-1/4) = sqr2 + 1, find the value of x^(1/2) + x^(-1/2) and x + x^(-1), leaving your answers in surd form.
Where do I begin? Thanks!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

You are given 

x^(1/4) + x^(-1/4) = sqrt%282%29+%2B+1.   (!)

Square both sides. You will get

x^(1/2) + 2x^(1/4)*x^(-1/4) + x^(-1/2) = %28sqrt%282%29%2B1%29%5E2,   or

x^(1/2) + 2 + x^(-1/2) = 2+%2B+2%2Asqrt%282%29%2B1.


Simplify:


x^(1/2) + x^(-1/2) = 2%2Asqrt%282%29%2B1.   (2)


So, this is the answer to your first question.


Now square (2) one more time and do the same.


I hope, you just got an idea that you are on the right road/rout.


Please complete it on your own, if you can.

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