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x² - 13x + 1 = 0
x(x - 13 + 1/x) = 0
x - 13 + 1/x = 0
x + 1/x = 13
x² + 1/x² + 2 = 169
x² + 1/x² = 167
Similarly, x^4 + 1/x^4 = 167² - 2, which last digit is 7.
x² - 13x + 1 = 0
x(x - 13 + 1/x) = 0
x - 13 + 1/x = 0
x + 1/x = 13
x² + 1/x² + 2 = 169
x² + 1/x² = 167
Similarly, x^4 + 1/x^4 = 167² - 2, which last digit is 7.