SOLUTION: if x=sqrt{3+2sqrt(2)} then find the value of x^2+1/x^2 and x+1/x

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Question 875151: if x=sqrt{3+2sqrt(2)} then find the value of x^2+1/x^2 and x+1/x
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x=sqrt%283%2B2sqrt%282%29%29
x%2B%281%2Fx%29=sqrt%283%2B2sqrt%282%29%2B1%29%2Fsqrt%283%2B2sqrt%282%29%29

=%283%2B2sqrt%282%29%2B1%29%2F%28sqrt%283%2B2sqrt%282%29%29%29
=%284%2B2sqrt%282%29%29%2F%28sqrt%283%2B2sqrt%282%29%29%29

%28x%5E2%2B%281%2Fx%5E2%29%29=+%28x%2B%281%2Fx%29%29%5E2-2
=%28%284%2B2sqrt%282%29%29%2F%28%28sqrt%283%2B2sqrt%282%29%29%29%29%29%5E2-2
further you may rationalize the denominator and simplify

=%28%2824%2B16sqrt%282%29%29%2F%28%283%2B2sqrt%282%29%29%29%29-2