Show that ${{x}^{2}}+2x+2$ is always positive for all real values of $x$.[1] Without using

Question

Show that ${{x}^{2}}+2x+2$ is always positive for all real values of $x$.[1] Without using a calculator, solve the inequality $\frac{x-12}{{{x}^{2}}+3x-10}>1$.[3]

Accepted Answer

(i) Since ${{\left( x+1 \right)}^{2}}\ge 0$ for all $x\in \mathbb{R}$, ${{\left( x+1 \right)}^{2}}+1>0$ for all $x\in \mathbb{R}$. (ii) $-5 < x < 2$

2022 VJC Promo Q2

2022 VJC Promo Q2

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