Question

Split 207 into three parts such that these are in A.P. and the product of the two smaller parts is 4623.

Answer 1

Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).

$$\begin{gathered} a-d+a+a+d=207 \\ \Rightarrow 3a=207 \\ \Rightarrow a=69 \\ \mathrm{Now},\left(a-d\right)\times a=4623 \\ \Rightarrow 69\left(69-d\right)=4623 \\ \Rightarrow \left(69-d\right)=67 \\ \Rightarrow d=2 \\ \mathrm{Therefore},\mathrm{the}\mathrm{three}\mathrm{required}\mathrm{parts}\mathrm{are}67,69\mathrm{and}71. \end{gathered}$$