Question

If | z – 4 + 3i | ≤ 1 and m and n 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 =

• A. n
• B. m
• C. m + n
• D. None of these

Answer 1

Answer: (A)

n

Answer 2

Sol. $\left| |\text{ z }|\text{ }\text{–}\text{ }|\text{ 4 }\text{–}\text{ 3i }| \right|$≤ | z – 4 + 3i | ≤ | z | + | – 4 + 3i |

Ž $\left| |\text{ z }|\text{ }\text{–}\text{5 } \right|$ ≤ 1 Ž 4 £ | z | £ 6 i.e. m = 4, n = 6

also y =$\frac{x^{4} + x^{2} + 4}{x}$, x Ī (0, ) has least value '6'.