If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

Answer

N/a

Explanation

Let three numbers in A.P. are a-d, a and a + d.
`therefore` (a - d) + a + (a + d) = 24
`rArr` 3a = 24
`rArr` a = 8
Product of numbers `= (a - d) a (a + d) = a (a^(2) - d^(2))`
` = a^(3) - ad^(2)`
`therefore` `a^(3) - ad^(2) = 440`
`rArr` `(8)^(3) - 8d^(2) = 440`
`rArr` `512 - 8d^(2) = 440`
`rArr` `- 8d^(2) = 440 - 512 = - 72`
`rArr` `d^(2) = 9 " " rArr " " d = +- 3`
`{:(d = 3 " then"),("First number " = a - d),(=8 - 3 = 5),("Second number " = u = 8),("Third number " = a + d),(= 8 + 3 = 11):}:|{:(d = -3 " then,"),("First number " = 8 - (-3) = 11),("Second number " = 8),("Third number " = 8 - 3),(= 5):}`
Therefore, numbers are 5, 8, 11 or 11, 8, 5.