If x^2-3x +3=0, find (x-1)^16+ 1/(x-1)^16
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Answer:
65536.00001525879.
Step-by-step explanation:
x² - 3x + 3 = 0
(x-1)(x-3) = 0
x = 1 or 3.
when x = 1,
(x-1)¹⁶ + 1/(x-1)¹⁶ = 0 + 1/0 is invalid
when x = 3,
(3-1)¹⁶ + 1/(3-1)¹⁶ = 2¹⁶ + 1/2¹⁶ = 65536.00001525879.
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