How to solve this Math Olympiad Problem | Here is a simple and easy solution

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I get it but i would have never thought of that. How do you get the intuition behind these? I would love to learn the trick to know the answer. Thank you for these videos.

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Lot of thanks as always
(a+b)³=a³+b³+3(a.b)(a+b)
--/--
(x+1/x)³ =
x³+1/x³+3(x•1/x)(x+1/x)
=
[x³+1/x³+3(x+1/x)]

--
(x+1/x)²= x²+1/x² +2(x•1/x)
=
[x²+1/x²+2]

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