x1+x2=-b/a --------------------(1)
x1x2=c/a --------------------------(2)
x1:x2=2:3,则:
x1=(2/3)x2,分别代入(1)、(2),得:
(2/3)x2+x2=-b/a
(2/3)x2²=c/a
即:
x2=-(3b)/(5a)
x2²=(3c)/(2a)
则:
[-(3b)/(5a)]²=(3c)/(2a)
(9b²)/(25a²)=(3c)/(2a)
(3c)×(25a²)=(9b²)×(2a)
6b²=25ac