Q.253. Simple but tricky algebra question.

Question 253.
Find x^6 + 1, if (x + 1/x)^2 = 3.

Answer 253.
(x + 1/x)^2 = 3
=> x^2 + 2 + 1/x^2 = 3
=> x^4 - x^2 + 1 = 0

x^6 + 1
= (x^2)^3 + 1
= (x^2 + 1)(x^4 - x^2 + 1)
= (x^2 + 1) * 0
= 0.

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