2019-II-04 – Solving Master

答案：C

\begin{array}{rcl} (x - 8) (x + α) - 6 & \equiv & (x - 9)^{2} + β \\ x^{2} + (α - 8) x + (- 8 α - 6) & \equiv & x^{2} - 18 x + 81 + β \end{array}

透過比較兩方的係數，可得

${\begin{cases} α - 18 = - 18 & \dots ① \\ - 8 α - 6 = 81 + β & \dots ② \end{cases}$

從 $①$ ，可得

$\begin{array}{rcl} α - 8 & = & - 18 \\ α & = & - 10 \end{array}$

把 $α = - 10$ 代入 $②$ ，可得

$\begin{array}{rcl} - 8 (- 10) - 6 & = & 81 + β \\ β & = & - 7 \end{array}$