If $\left|z-4+3i\right|\le 1$and $\alpha$ and $\beta$ be the least and greatest value of $\left|z\right|\&K$be the least value of $\frac{x^4+x^2+4}{x}$on the interval $\left(0,\infty \right)$, then K=

Given that  $\left|z-4+3i\right|\le 1$

$\Rightarrow \left|z-(4-3i)\right|\le 1\Rightarrow 1\ge \left|z-(4-3i\right|\ge \left\{\begin{array}{l}\left|z\right|-\left|4-3i\right|\\ \left|4-3i\right|-\left|z\right|\end{array}\right\}$

$\therefore \left|z\right|\le 6\&\left|z\right|\ge 4[\therefore \left|4-3i\right|=5]\Rightarrow 4\le \left|z\right|\le 6$

$x^3=x=\frac{1}{x}\Rightarrow x=1_{as}y=x^3+x+\frac{4}{x}$

$i.e\alpha =4\&\beta =6\therefore y\left(least\right)=6\therefore K=6,soK=\beta$