Question

If x=3+2√2, find the value of x2+1/x2

Answer 1

Answer:

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Step-by-step explanation:

x = 3+2√2

x^2 = (3+2√2)^2

x^2 = (3)^2 + 2(3)(2√2) + (2√2)^2

x^2 = 9+12√2+8

x^2 = 17+12√2  ------(1)

1/x^2 = 1/17+12√2           (putting value of x^2 from equation 1)

1/x^2 = multiplying and dividing by 17- 12√2 to rationalize the        denominator

So,  1/x^2 = 17-12√2  --------(2)

x^2 + 1/x^2  = 17 + 12√2 + 17 - 12√2  (putting values of x^2 and                  

                                                              1/x^2 from equation 1 and  

                                                               2)

x^2 + 1/x^2 = 17 + 17

x^2 + 1/x^2 = 34