\left|
{ ( 1 + α ) 2 ( 1 + 2 α ) 2 ( 1 + 3 α ) 2 ( 2 + α ) 2 ( 2 + 2 α ) 2 ( 2 + 3 α ) 2 ( 3 + α ) 2 ( 3 + 2 α ) 2 ( 3 + 3 α ) 2 \begin{cases}{\left(1 + \alpha\right)}^{2} & {\left(1 + 2\alpha\right)}^{2} & {\left(1 + 3\alpha\right)}^{2} \\ {\left(2 + \alpha\right)}^{2} & {\left(2 + 2\alpha\right)}^{2} & {\left(2 + 3\alpha\right)}^{2} \\ {\left(3 + \alpha\right)}^{2} & {\left(3 + 2\alpha\right)}^{2} & {\left(3 + 3\alpha\right)}^{2}\end{cases} ⎩ ⎨ ⎧ ( 1 + α ) 2 ( 2 + α ) 2 ( 3 + α ) 2 ( 1 + 2 α ) 2 ( 2 + 2 α ) 2 ( 3 + 2 α ) 2 ( 1 + 3 α ) 2 ( 2 + 3 α ) 2 ( 3 + 3 α ) 2 \right|
< b r > < b r > <br ><br > < b r >< b r > {R}_{2} \to {R}_{2} - {R}_{1}
( T a k e c o m m o n ) < b r > (Take common) <br > ( T ak eco mm o n ) < b r > {R}_{3} \to {R}_{3} - {R}_{1}
< b r > < b r > <br ><br > < b r >< b r > 2\left|
{ ( 1 + α ) 2 ( 1 + 2 α ) 2 ( 1 + 3 α ) 2 3 + 2 α ( 3 + 4 α ) ( 3 + 6 α ) ( 4 + 2 α ) ( 4 + 4 α ) ( 4 + 6 α ) \begin{cases}{\left(1 + \alpha\right)}^{2} & {\left(1 + 2\alpha\right)}^{2} & {\left(1 + 3\alpha\right)}^{2} \\ 3 + 2\alpha & \left(3 + 4\alpha\right) & \left(3 + 6\alpha\right) \\ \left(4 + 2\alpha\right) & \left(4 + 4\alpha\right) & \left(4 + 6\alpha\right)\end{cases} ⎩ ⎨ ⎧ ( 1 + α ) 2 3 + 2 α ( 4 + 2 α ) ( 1 + 2 α ) 2 ( 3 + 4 α ) ( 4 + 4 α ) ( 1 + 3 α ) 2 ( 3 + 6 α ) ( 4 + 6 α ) \right|
< b r > < b r > <br ><br > < b r >< b r > {R}_{3} \to {R}_{3} - {R}_{2}
< b r > < b r > <br ><br > < b r >< b r > 2\left|
{ ( 1 + α ) 2 ( 1 + 2 α ) 2 ( 1 + 3 α ) 2 3 + 2 α 3 + 4 α 3 + 6 α 1 1 1 \begin{cases}{\left(1 + \alpha\right)}^{2} & {\left(1 + 2\alpha\right)}^{2} & {\left(1 + 3\alpha\right)}^{2} \\ 3 + 2\alpha & 3 + 4\alpha & 3 + 6\alpha \\ 1 & 1 & 1\end{cases} ⎩ ⎨ ⎧ ( 1 + α ) 2 3 + 2 α 1 ( 1 + 2 α ) 2 3 + 4 α 1 ( 1 + 3 α ) 2 3 + 6 α 1 \right|
< b r > < b r > <br ><br > < b r >< b r > {C}_{2} \to {C}_{2} - {C}_{1}
( T a k e c o m m o n ) < b r > (Take common) <br > ( T ak eco mm o n ) < b r > {C}_{3} \to {C}_{3} - {C}_{1}
< b r > < b r > <br ><br > < b r >< b r > ∴ 2\alpha2 . \alpha
\left| \begin{cases}{\left(1 + \alpha\right)}^{2} & \left(2 + 3\alpha\right) & \left(2 + 4\alpha\right) \\ 3 + 2\alpha & 2 & 2 \\ 1 & 0 & 0\end{cases}
\right| 4 α 2 ∣ − 2 α ∣ 4{\alpha}^{2}\left|- 2\alpha\right| 4 α 2 ∣ − 2 α ∣ = - 8{\alpha}^{3} = - 648\alpha
< b r > <br > < b r > \alpha = 0, {\alpha}^{2} = 81, \alpha = \pm 9
