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in Arithmetic Progression by (29.9k points)
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Divide 24 in three parts such that they are in AP and their product is 440.

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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

\(\Rightarrow\) 3a = 24

\(\Rightarrow\) a = 8

Also, (a - d).a.(a + d) = 440

\(\Rightarrow\) a(a2 - d2) = 440

\(\Rightarrow\) 8(64 - d2) = 440

\(\Rightarrow\) d2 = 64 - 55 = 9

\(\Rightarrow\) d = \(\pm3\)

Thus, a = 8 and d = \(\pm3\)

Hence, the required parts of 24 are (5,8,11) or (11,8,5).

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