The roots α, β and γof an equation x3−3ax2+3bx−c=0 are in H.P. Then,

Given that the roots of the equation x3−3ax2+3bx−c=0 are in H.P. Therefore, the roots of the reciprocal equation i.e. cy3−3by2+3ay−1=0 are in A.P.i.e. 1α,1β,1γ are in A.P.2β=1α+1γ⇒ 3β=1α+1β+1γ⇒3β=3bc⇒β=cb      ∵1α+1β+1γ=3bc