Gọi x1, x2 (x1, x2) là hai nghiệm của phương trình |x^2-4x-5|=4x-17

* Hướng dẫn giải

Phương trình $\iff \left\{\begin{array}{c}4x-17\ge 0\\ \left|x^2-4x-5\right|={\left(4x-17\right)}^2\end{array}\right.$

$\iff \left\{\begin{array}{c}x\ge \frac{17}{4}\\ {\left(x^2-5x-5\right)}^2={\left(4x-17\right)}^2\end{array}\right.$

$\begin{array}{l}\iff \left\{\begin{array}{c}x\ge \frac{17}{4}\\ (x^2-8x+12)(x^2-22)=0\end{array}\right.\iff \left\{\begin{array}{c}x\ge \frac{17}{4}\\ \left[\begin{array}{c}{x}^2-8x+12=0\\ x^2-22=0\end{array}\right.\end{array}\right.\end{array}$

$\begin{array}{l}\iff \left\{\begin{array}{c}x\ge \frac{17}{4}\\ \left[\begin{array}{c}x=2\vee x=6\\ x=\pm \sqrt{22}\end{array}\right.\end{array}\right.\iff \left[\begin{array}{c}x=6\\ x=\sqrt{22}\end{array}\right.\\ \Rightarrow P={\left(\sqrt{22}\right)}^2+6=28\end{array}$

Đáp án cần chọn là: C