Way too easier than last year.
Write the full solution.
1.) Let be real numbers such that . Find the maximum value of .
2.) If , prove that .
3.) Find all roots of .
4.) (Someone posted this problem before in Brilliant.) Find all polynomials with real coefficients such that and
5.) If are positive real numbers such that . Find the value of .
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Thailand Math POSN 2013
Thailand Math POSN 2014