Đáp án:

Hệ số góc của đường thẳng d bằng 3 hoặc 4.

Giải thích các bước giải:

\(\eqalign{ & \left( P \right):\,\,y = 3{x^2} - 5x + 5 \cr & A\left( {2;a} \right) \in \left( P \right) \Rightarrow a = {3.2^2} - 5.2 + 5 = 7 \cr & \Rightarrow A\left( {2;7} \right) \cr & B\left( {b;3} \right) \Rightarrow 3 = 3{b^2} - 5b + 5 \cr & \Rightarrow 3{b^2} - 5b + 2 = 0 \Leftrightarrow \left[ \matrix{ b = {2 \over 3} \hfill \cr b = 1 \hfill \cr} \right. \Rightarrow \left[ \matrix{ B\left( {{2 \over 3};3} \right) \hfill \cr B\left( {1;3} \right) \hfill \cr} \right. \cr & TH1:\,\,d\,\,di\,\,qua\,\,A\left( {2;7} \right)\,\,va\,\,B\left( {{2 \over 3};3} \right) \cr & Goi\,\,d:\,\,y = mx + n \cr & A\left( {2;7} \right) \in d \Rightarrow 7 = 2m + n \cr & B\left( {{2 \over 3};3} \right) \in d \Rightarrow 3 = {2 \over 3}m + n \cr & \Rightarrow \left\{ \matrix{ m = 3 \hfill \cr n = 1 \hfill \cr} \right. \Leftrightarrow d:\,\,y = 3x + 1 \Rightarrow HSG = 3 \cr & TH2:\,\,d\,\,di\,\,qua\,\,A\left( {2;7} \right)\,\,va\,\,B\left( {1;3} \right) \cr & Goi\,\,d:\,\,y = mx + n \cr & A\left( {2;7} \right) \in d \Rightarrow 7 = 2m + n \cr & B\left( {1;3} \right) \in d \Rightarrow 3 = m + n \cr & \Rightarrow \left\{ \matrix{ m = 4 \hfill \cr n = - 1 \hfill \cr} \right. \Leftrightarrow d:\,\,y = 4x - 1 \Rightarrow HSG = 4 \cr} \)