YLL討論網

#ed_op#DIV#ed_cl#以x-y，y-z為根的方程#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#t^2+(z-x)t+(x-y)(y-z)=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#由已知有重根#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#x-y=y-z#ed_op#/DIV#ed_cl#

原式=








表示y為等差中項,所以x,y,z成AP.

#ed_op#DIV#ed_cl#if (z-x)^2=4(x-y)(y-z)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#證明x，y，z成等差#ed_op#/DIV#ed_cl#