a2+3a-1=0 b2+3b-1=0,则b/a+a/b=
问题描述:
a2+3a-1=0 b2+3b-1=0,则b/a+a/b=
答
a2+3a-1=0 b2+3b-1=0
可以看成 x2+3x-1=0的两根为a,b
x1+x2=a+b=-3
x1*x2=ab= -1
b/a+a/b=(a2+b2)/ab
=[(a+b)2-2ab]/ab
=(9+2)/(-1)
=-11答案给的是2或-11!当a=b时,b/a+a/b=1+1=2当a≠b,时可以看成 x2+3x-1=0的两根为a,bx1+x2=a+b=-3x1*x2=ab= -1b/a+a/b=(a2+b2)/ab =[(a+b)2-2ab]/ab =(9+2)/(-1) =-11