Question:
Divide 24 in three parts such that they are in AP and their product is 440.
Solution:
Let the required parts of 24 be (a - d), a and (a + d) such that they are in AP.
Then (a - d) + a + (a + d) = 24
⇒ 3a = 24
⇒ a = 8
Also, (a - d).a.(a + d) = 440
$\Rightarrow a\left(a^{2}-d^{2}\right)=440$
$\Rightarrow 8\left(64-d^{2}\right)=440$
$\Rightarrow d^{2}=64-55=9$
$\Rightarrow d=\pm 3$
Thus, $a=8$ and $d=\pm 3$
Hence, the required parts of 24 are (5, 8,11) or (11, 8, 5).