Question

14．若x-y=2，x²+y²=4，则x²⁰⁰⁸+y²⁰⁰⁸=2²⁰⁰⁸．

Answer 1

分析 联立$\left\{\begin{array}{l}{x-y=2}\\{{x}^{2}+{y}^{2}=4}\end{array}\right.$，解得x，y，代入即可得出．

解答 解：联立$\left\{\begin{array}{l}{x-y=2}\\{{x}^{2}+{y}^{2}=4}\end{array}\right.$，解得$\left\{\begin{array}{l}{x=2}\\{y=0}\end{array}\right.$或$\left\{\begin{array}{l}{x=0}\\{y=-2}\end{array}\right.$．
∴x²⁰⁰⁸+y²⁰⁰⁸=2²⁰⁰⁸，
故答案为：2²⁰⁰⁸．

点评 本题考查了方程组的解法、代数式的计算，考查了计算能力，属于基础题．