Question

16．二元二次方程组$\left\{\begin{array}{l}{x+y=3}\\{xy=-10}\end{array}\right.$的解是（　　）

• A． $\left\{\begin{array}{l}{{x}_{1}=-5}\\{{y}_{1}=2}\end{array}\right.$   $\left\{\begin{array}{l}{{x}_{2}=2}\\{{y}_{2}=-5}\end{array}\right.$
• B． $\left\{\begin{array}{l}{{x}_{1}=5}\\{{y}_{1}=2}\end{array}\right.$   $\left\{\begin{array}{l}{{x}_{2}=2}\\{{y}_{2}=5}\end{array}\right.$
• C． $\left\{\begin{array}{l}{{x}_{1}=5}\\{{y}_{1}=-2}\end{array}\right.$   $\left\{\begin{array}{l}{{x}_{2}=-2}\\{{y}_{2}=5}\end{array}\right.$
• D． $\left\{\begin{array}{l}{{x}_{1}=-5}\\{{y}_{1}=-2}\end{array}\right.$   $\left\{\begin{array}{l}{{x}_{2}=-2}\\{{y}_{2}=-5}\end{array}\right.$

Answer 1

分析 将x、y看作是一元二次方程a²-3a-10=0的两个根，故只需求出该方程的解即可．

解答 解：由题意可知：x、y是一元一次方程a²-3a-10=0的两个根，
∵a²-3a-10=（a-5）（a+2）=0
∴a₁=5，a₂=-2
故：选C

点评 本题考查了一元二次方程的根与系数的关系的变相应用问题，解题的关键是将$\left\{\begin{array}{l}{x+y=3}\\{xy=-10}\end{array}\right.$的解x、y看作是一元二次方程a²-3a-10=0的两个根从而更简便地解决问题．