Hàm số \(y{\rm{\;}} = {\rm{\;}}\left( {{a^2}\;-{\rm{\;}}4} \right){x^2}\; + {\rm{\;}}\left( {b{\rm{\;}}-{\rm{\;}}3a} \right)\left( {b{\rm{\;}} + {\rm{\;}}2a} \right)x{\rm{\;}}-{\rm...

* Hướng dẫn giải

Hàm số \(y{\rm{\;}} = {\rm{\;}}\left( {{a^2}-{\rm{\;}}4} \right){x^2} + {\rm{\;}}\left( {b{\rm{\;}}-{\rm{\;}}3a} \right)\left( {b{\rm{\;}} + {\rm{\;}}2a} \right)x{\rm{\;}}-{\rm{\;}}2\) là hàm số bậc nhất khi:

\(\left\{ {\begin{array}{*{20}{l}}
{{a^2} - 4 = 0}\\
{\left( {b - 3a} \right)\left( {b + 2a} \right) \ne 0}
\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}
{\left[ {\begin{array}{*{20}{l}}
{a = 2}\\
{a =  - 2}
\end{array}} \right.}\\
{b \ne 3a}\\
{b \ne  - 2a}
\end{array}} \right.\)

Với \(a\; = \;2\;\; \Rightarrow \left\{ {\begin{array}{*{20}{l}}
{b \ne 6}\\
{b \ne  - 4}
\end{array}} \right.\)

Với \(a\; = \; - 2 \Rightarrow \left\{ {\begin{array}{*{20}{l}}
{b \ne  - 6}\\
{b \ne 4}
\end{array}} \right.\)