If x3 - 4x2 + 19 = 6(x - 1) then what is the value of [ x^2 + 1x - 4 ]?

Answer: Option C

$$\begin{array}{rl}& x^3-4x^2+19=6\left(x-1\right)......\left(1\right)\left(\text{Given}\right)\\ & \&\left(x^2+\frac{1}{x-4}\right)=?\left(\text{To find}\right)\\ & \to \frac{x^2\left(x-4\right)+1}{x-4}......\left(2\right)\\ & \text{from equation}\left(1\right)\\ & x^3-4x^2+19=6x-6\\ & x^3-4x^2+1+18=6x-6\\ & x^3-4x^2+1=6x-6-18\\ & x^3-4x^2+1=6x-24\\ & \text{putting the value of }\left(x^3-4x^2+1\right)\text{in equation }\left(2\right)\\ & \text{we get,}=\frac{6x-24}{x-4}=\frac{6\left(x-4\right)}{\left(x-4\right)}=6\end{array}$$