Question

15．若$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$都是方程ax-by=4的解，求代數(shù)式（b-a）²⁰¹²的值．

Answer 1

分析 根據(jù)題意直接將$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$代入方程ax-by=4，求出a，b的值進(jìn)而得出答案．

解答 解：∵$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$都是方程ax-by=4的解，
∴$\left\{\begin{array}{l}{a+2b=4}\\{2a=4}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$，
∴（b-a）²⁰¹²=1．

點評 此題主要考查了二元一次方程組的解法，得出關(guān)于a，b的方程組是解題關(guān)鍵．