2016 SAJC Promo Q3

2016 SAJC Promo Q3

7 marks

Promo

Solve the inequality, leaving your answers in exact form, \(\left| 1+\frac{x}{2} \right|>5-{{x}^{2}}\).[4]
Hence solve \(\left| 1-\frac{{{e}^{x}}}{2} \right|>5-{{e}^{2x}}\).[3]

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Answer:(i) x < (1-√97)/4 or x > (-1+√65)/4; (ii) x > ln((√97-1)/4)

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