Question

The equation $2^{\frac{2\pi}{\cos^{- 1}x}}$– $\left( a + \frac { 1 } { 2 } \right)$ $2^{\frac{\pi}{\cos^{- 1}x}}$– a² = 0 has only one real root, then –

• A. a Ī [1, 3]
• B. a Ī (–,–3] Č [1, )
• C. a Ī (1, 3)
• D. None of these

Answer 1

Answer: (B)

a Ī (–,–3] Č [1, )

Answer 2

1 £ $\frac{\pi}{\cos^{- 1}x}$<  Ž 2 £ $2^{\pi/\cos^{- 1}x}$< 

Hence 2 should lie between roots of

t² – $\left( a + \frac{1}{2} \right)$t – a² = 0

where t = $2^{\frac{\pi}{\cos^{- 1}x}}$

a² + 2a – 3 ³ 0

\ a Ī (–, –3] Č [1, )