Complexificaton of algebra

Algebra Level 4

If ∣ z − 4 + 3 i ∣ ≤ 1 |z-4+3i| \leq 1 and α , β \alpha, \beta be the least and the greatest value of ∣ z ∣ |z| respectively and k k be the least value of x 4 + x 2 + 4 x \large \frac{x^4 + x^2 +4}{x} on the interval ( 0 , ∞ ) (0,\infty) , then what is the value of k k .

This is not a original problem.

beeta 0 alpha none

Akshay Sharma by Akshay Sharma , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Deepak Kumar
Jan 15, 2016

Hint:The inequality represents all points on or within a circle with center (4,-3) and radius 1 which gives min|z|=4 and max|z|=6.Further 'k' can be obtained by use of AM-GM (taking terms of the expression as sum of x^3,x,1/x,1/x,1/x,1/x )and comes out to be 6.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...