計算1
跟著鋼琴老師的答案，試著把這5分的計算1(a)的過程寫出來。
\[b\begin{vmatrix} x&x^{3}+ax^{2} &1 \\ y&y^{3}+ay^{2} &1 \\ z&z^{3}+az^{2} &1 \end{vmatrix} =\begin{vmatrix} x-y &x^{3}+ax^{2}-y^{3}-ay^{2} &0\\ y-z &y^{3}+ay^{2}-z^{3}-az^{2} &0 \\ z & z^{3}+az^{2} &1 \end{vmatrix}\]
\[=b[(x-y)(y^{3}+ay^{2}-z^{3}-az^{2})-(y-z)(x^{3}+ax^{2}-y^{3}-ay^{2})]\]
\[=b\left \{ \left ( x-y\left \lfloor \left ( y-z \right )\left ( y^{2}+yz+z^{2} \right )+a\left ( y-z \right )\left ( y+z \right ) \right \rfloor \right ) \right \}-\left ( y-z\left \lfloor \left ( x-y \right )\left ( x^{2}+xy+y^{2} \right )+a\left ( x-y \right )\left ( x+y \right ) \right \rfloor \right )\]
\[=b\left (x-y \right )\left ( y-z \right )\left [ y^{2}+yz+z^{2}+ay+az-x^{2}-xy-y^{2}-ax-ay \right ]\]
\[=b\left ( x-y \right )\left ( y-z \right )\left [ a\left ( z-x \right )+y\left ( z-x \right )+\left ( z^{2}-x^{2} \right ) \right ]\]
\[=b\left ( x-y \right )\left ( y-z \right )\left ( z-x \right )\left ( a+x+y+z \right )\]
[ 本帖最後由 mojary 於 2018-6-21 13:30 編輯 ]
