Question

20．已知關(guān)于a，b，c的單項(xiàng)式$\frac{1}{2}$a^x+y-zb^x+z-yc^z與-$\frac{1}{2}$a¹¹b^y+z-xc的和等于0，求x，y，z的值．

Answer 1

分析 根據(jù)但相識(shí)的和為零，可得同類項(xiàng)，根據(jù)同類項(xiàng)的定義，可得方程組，根據(jù)解方程組，可得答案．

解答 解：由關(guān)于a，b，c的單項(xiàng)式$\frac{1}{2}$a^x+y-zb^x+z-yc^z與-$\frac{1}{2}$a¹¹b^y+z-xc的和等于0，得
$\left\{\begin{array}{l}{x+y+z=11}\\{x+z-y=y+z-x}\\{z=1}\end{array}\right.$，解得$\left\{\begin{array}{l}{x=5}\\{y=5}\\{z=1}\end{array}\right.$．

點(diǎn)評(píng) 本題考查了合并同類項(xiàng)，利用同類項(xiàng)的定義得出方程組是解題關(guān)鍵．