Show that $\frac{3}{2}-\sqrt{a+\frac{1}{4}}[1] Solve the inequality $\frac{{{x}^{2}}-x-a}{x-1}\le 2$

Question

Show that $\frac{3}{2}-\sqrt{a+\frac{1}{4}}[1] Solve the inequality $\frac{{{x}^{2}}-x-a}{x-1}\le 2$, where $a$ is a positive constant. [4] Hence solve $\frac{a+x-{{x}^{2}}}{x}\le 2$ . [2]

Accepted Answer

(i) shown; (ii) x ≤ 3/2 - √(a+1/4) or 1 < x ≤ 3/2 + √(a+1/4); (iii) -(1+√(1+4a))/2 ≤ x < 0 or x ≥ (√(1+4a)-1)/2

2018 HCI P1 Q4

2018 HCI P1 Q4

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