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Hanoi Open Mathematics Competition 2012 Senior Question 2

HOMC · Hanoi Open Mathematics Competition 2012 Senior

Question 2

Compare \(P=2^\alpha,Q=3,T=2^\beta\), where \(\alpha=\sqrt2\), \(\beta=1+\dfrac1{\sqrt2}\).
  1. \(P\lt Q\lt T\)
  2. \(T\lt P\lt Q\)
  3. \(P\lt T\lt Q\)
  4. \(T\lt Q\lt P\)
  5. \(Q\lt P\lt T\)