IP3U2 HOT PN1 Q4

IP3U2 HOT PN1 Q4

IP 3

Solve the inequality \(\frac{2x-{{x}^{2}}-5}{(x+1)(x-3)}\le 0\). Hence, solve the following inequalities:

  1. \(\frac{2x-{{(x+2)}^{2}}-1}{(x+3)(x-1)}\le 0\)
  2. \(\frac{2\left| x \right|-{{x}^{2}}-5}{(\left| x \right|+1)(\left| x \right|-3)}\le 0\)
  3. \(\frac{2{{x}^{2}}-{{x}^{4}}-5}{({{x}^{2}}+1)({{x}^{2}}-3)}\le 0\)

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Answer:Main: \(x<-1\) or \(x>3\) (i) \(x<-3\) or \(x>1\) (ii) \(x<-3\) or \(x>3\) (iii) \(x<-\sqrt3\) or \(x>\sqrt3\)

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