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How to do the 22 nd question on page 88 of the second volume of the first mathematics experimental class of Zhejiang Education Edition?
From the solution of x 2-3x+ 1 = 0, it is found that x 1 = (3+√ 5)/2 and x2 = (3-√ 5)/2.

x ^2+ 1/x^2= x 1^2+ 1/x 1^2 = x 2^2+ 1/x2^2= 7

x ^4+ 1/x^4=(x ^2+ 1/x^2)^2- 2 = 47