Tìm m để đồ thị $(C):x^{3}+(5-m)x^{2}+(6-5m)x-6m $ cắt trục hoành tại 3 điểm có hoành độ độc lập lập thành cấp số nhân.
      

giả sử đồ thị cắt trục hoành tại 3 điểm $x_1; x_2; x_3$
khi đó có 
$y=(x-x_1)(x-x_2)(x-x_3)=x^3-(x_1 +x_2 +x_3 )x^2+(x_1 x_2 + x_2 x_3 +x_3 x_1)x-x_1 x_2 x_3$
viét:
$x_1 +x_2 +x_3=m-5$
$x_1 x_2 +x _2 x_3 +x_3 x_1=6-5m$                         (1)
$x_1 x_2 x_3=-6m$
theo đề tạo thành 1 csn:
$x_2^2=x_1 x_3$      (2) 
từ (1) và (2) sẽ dc m

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