Question

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Answer 1

Let the 3 numbers in A.P. are
a - d, a, a + d
Then,
$\Rightarrow a-d+a+a+d=27\Rightarrow 3a=27$
$\therefore a=9\dots \dots \left(i\right)$
and $(a-d)\left(a\right)(a+d)=648$
$(9-d)\left(9\right)(9-d)=648$ $[\because a=9]$
$9^2-d^2=72d^2=9\therefore d=\pm 3\dots \dots \left(ii\right)$
When a = 9, d = 3, we have, 6, 9, 12
When a = 9, d = -3, we have, 12, 9, 6