已知实数x,y满足x^2+√2y=√3,y^2+√2x=√3,求x+y和xy的值

题目

已知实数x,y满足x^2+√2y=√3,y^2+√2x=√3,求x+y和xy的值

答案

⑴若x＝y,则x、y是方程m^2＋√2m＝√3的两个相等实根由根与系数关系得：x＋y＝－√2,xy＝－√3⑵若x≠y,两式相减得：x^2－y^2＋√2y－√2x＝0,(x＋y－√2)(x－y)＝0得：x＋y＝√2两式再相加得：x^2＋y^2＋√2y＋√2x...