2025 MI PU1 Promo Q5

2025 MI PU1 Promo Q5

Junior College 1
7 marks
  1. Show that \(x^2-6x+13\) is positive for all real values of \(x\).[2]
  2. Hence, solve algebraically the inequality \(\frac{x^2-6x+13}{x^2-5x-6}<0\).[3]
  3. Deduce the solution to \(\frac{e^{2x}-6e^x+13}{e^{2x}-5e^x-6}<0\).[2]

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Answer:\(-1<x<6\); after substitution, \(x<\ln6\)

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