Question

The sum of three no.in Ap.is -24 and their product is 288. Find the numbers.

Answer 1

let
x, x+d, x + 2d are the numbers which are in A.P

given, sum of numbers = -24

x + x + d + x + 2d = -24

3x + 3d = -24

x + d = -8
x = -8 - d---»»» ●● 1

product of numbers = 288

x(x+d)(x+2d) = 288. -----»»»●● 2

from 1

(-8 - d) (-8)(-8+d) = 288


(d+8) (8) (d-8) = 288
(d+8)(d-8) = 36

d² - 8² = 36
d² = 100

d = +10. and. - 10
consider -10 to ful fill the given conditions

from 1
x = -8 - (-10) = 2
x + d = -8
x+2d = -8-10= -18

2, -8, -18

Hope you understand
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