2023 RI Promo Q2
2023 RI Promo Q2
8 marks
Promo
Do not use a calculator in answering this question.
Solve the inequality \({{x}^{2}}+6x+5\le \frac{x+5}{3x+1}\).[4]
Hence solve
- \({{x}^{4}}+6{{x}^{2}}+5\le \frac{{{x}^{2}}+5}{3{{x}^{2}}+1}\),[2]
- \({{\left( \ln x \right)}^{2}}+6\ln x+5\le \frac{5+\ln x}{1+3\ln x}\).[2]
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Answer:\(-5\leq x\leq-\dfrac43\) or \(-\dfrac13<x\leq0\) (a) \(x=0\) (b) \(e^{-5}\leq x\leq e^{-4/3}\) or \(e^{-1/3}<x\leq1\)
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