Inequalities - Inequalities involving Substitution

Inequalities - Inequalities involving Substitution

Solve the inequality \(\frac{x^2 - 6x + 11}{x^2 - 5x + 6} \ge 0\). Hence, solve the following inequalities:

  1. \(\frac{(x - 3)^2 - 6x + 29}{(x - 3)^2 - 5x + 21} \ge 0\)
  2. \(\frac{x^2 - 6|x| + 11}{x^2 - 5|x| + 6} \ge 0\)
  3. \(\frac{(\ln x)^2 - 6\ln x + 11}{(\ln x)^2 - 5\ln x + 6} \ge 0\)
  4. \(\frac{e^{2x} - 6e^x + 11}{e^{2x} - 5e^x + 6} \ge 0\)

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Answer:\(x < 2 \) or \( x > 3 \)

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