Question

Divide 24 in three parts such that they are in AP and their product is 440.

Answer 1

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
⇒ a(a² - d²) = 440​
⇒ 8​(64​​ -d²) = 440​ ​
⇒ d² = 64 - 55 = 9
⇒ d = $\pm$3
Thus, a = 8 and d = $\pm$3
Hence, the required parts of 24 are (5, 8,11) or (11, 8, 5).