2024 VJC Promo Q2

2024 VJC Promo Q2

5 marks
  1. Without using a calculator, solve the inequality \(\frac{2x^2 + 3x + 10}{x^2 - x} \ge 2\).[3]
  2. Hence, find the set of values of \(x\) for which \(\frac{2\mathrm{e}^{2x} - 3\mathrm{e}^x + 10}{\mathrm{e}^{2x} + \mathrm{e}^x} \ge 2\).[2]

Solution:

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Answer:(a) \([-2,0)\cup(1,\infty)\). (b) \(x\le\ln2\).

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