Question

If |z – 4 + 3i| £ 1 and a and b be the least and greatest values of |z| and k be the least value of $\frac{x^{4} + x^{2} + 4}{x}$on the interval (0, ) then k is equal to –

• A. a
• B. b
• C. a + b
• D. None of these

Answer 1

Answer: (B)

b

Answer 2

Sol. from |z – 4 + 3i| £ 1

Ž |z|_max= 6, |z|_min= 4

So a = 4, b = 6

y = $\frac{x^{4} + x^{2} + 4}{x}$= x³ + x + $\frac{4}{x}$

For y to be least x = 1

Ž y = 6 Ž y = b Ž k = b