Question

The sum of the three numbers in A.P is and their product is 231 find the number

Answer 1

Let the numbers be a−d,aa−d,a and a+da+d, clearly dd is the common difference.So, a−d+a+a+d=21⟹3a=21⟹a=7a−d+a+a+d=21⟹3a=21⟹a=7and a(a−d)(a+d)=231⟹7(72−d2)=231a(a−d)(a+d)=231⟹7(72−d2)=231 ⟹72−d2=33⟹d2=16⟹d=±4⟹72−d2=33⟹d2=16⟹d=±4So, the numbers are 7,7±47,7±4 i.e, 3,7,11