已知实数a,b分别满足a²-3a+根号下5=0,b-3b+根号下5=0,试求a/b+b/a
问题描述：
已知实数a,b分别满足a²-3a+根号下5=0,b-3b+根号下5=0,试求a/b+b/a
答
a,b为方程x^2-3x+√5=0的两个根 则a+b=3,ab=√5 a/b+b/a =(a^2+b^2)/(ab) =[(a+b)^2-2ab]/(ab) =(9-2√5)/√5 =(9√5-10)/5