Given that $x$ is real, prove algebraically that ${{x}^{2}}-2x+3$ is always positive. [1] Hence, wit

Question

Given that $x$ is real, prove algebraically that ${{x}^{2}}-2x+3$ is always positive. [1] Hence, without using a graphing calculator, find the range of values of $x$ that satisfy $\frac{x+4}{{{x}^{2}}-2x+3}\ge \frac{3}{2-x}$ [5]

Accepted Answer

$x = \frac{1}{2} or x > 2$

2016 MJC Promo Q1

2016 MJC Promo Q1

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