Using an algebraic method, solve the inequality $\displaystyle \frac{2x^2+17x+37}{x^2+3x-10}\leq1$

Question

Using an algebraic method, solve the inequality $\displaystyle \frac{2x^2+17x+37}{x^2+3x-10}\leq1$ exactly.[3] Hence, solve $\displaystyle \frac{2x^2+17|x|+37}{x^2+3|x|-10}\leq1$.[2]

Accepted Answer

(i) $x\in[-7-\sqrt2,-7+\sqrt2]\cup(-5,2)$ (ii) $-2<x<2$

2026 ASRJC P1 Q2

2026 ASRJC P1 Q2

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