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

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

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

Answer»

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).