Question

8．解方程组：$\left\{\begin{array}{l}{x-y=2}\\{{x}^{2}-2xy-{y}^{2}=0}\end{array}\right.$．

Answer 1

分析 根据解方程组的方法可以解答此方程．

解答 解：由$\left\{\begin{array}{l}{x-y=2}\\{{x}^{2}-2xy-{y}^{2}=0}\end{array}\right.$得
$\left\{\begin{array}{l}{x-y=2}&{①}\\{（x-y）^{2}-2{y}^{2}=0}&{②}\end{array}\right.$
将①代入②，得
4-2y²=0
解得，y=$±\sqrt{2}$，
将y=$\sqrt{2}$代入①，得
x=2+$\sqrt{2}$，
将x=-$\sqrt{2}$代入②，得
x=2-$\sqrt{2}$，
故原方程组的解是$\left\{\begin{array}{l}{x=2+\sqrt{2}}\\{y=\sqrt{2}}\end{array}\right.$或$\left\{\begin{array}{l}{x=2-\sqrt{2}}\\{y=-\sqrt{2}}\end{array}\right.$．

点评 本题考查解高次方程，解题的关键是明确解方程组的方法．