Without using a calculator, solve the inequality $\frac{{{x}^{2}}-3x+4}{x+2}\ge 2x+1$. Hence solve t

Question

Without using a calculator, solve the inequality $\frac{{{x}^{2}}-3x+4}{x+2}\ge 2x+1$. Hence solve the inequality $\frac{{{a}^{2x}}+3{{a}^{x}}+4}{{{a}^{x}}-2}\le 2{{a}^{x}}-1$ where $a>2$. [6]

Accepted Answer

(i) $x \leq -4 - 3\sqrt{2}$ or $-2 < x \leq -4 + 3\sqrt{2}$ (ii) $x \geq \frac{\ln(4 + 3\sqrt{2})}{\ln a}$ or $x < \frac{\ln 2}{\ln a}$

2019 NYJC P1 Q3

2019 NYJC P1 Q3

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