Question

find three positive integers in A. P. such that sum is 24 and product is 480​

Answer 1

Answer :- 2

Explaination:-

Answer 2

Answer:

6,8,10  (or) 10,8,6

Step-by-step explanation:

Let the nos. in A.P be x,y,z.

the A.P is a-d, a, a+d.

SUM:

x+y+z = a-d + a +a+d

         24 = 3a

         a  = 8 (24/3)

PRODUCT:

xyz = (a-d)(a)(a+d)

     Substitute a=8

          =  (8-d)(8)(8+d)

          =  ( 8² - d²) (8)

           = (64 - d²) (8)

480 /8    = 64 - d²

60      =    64 - d²

60-64 = -d²

-4 = -d²  ( Both sides minus cancelled)

4 = d²

d= ± 2

The integers are :

if d= 2                                              if d=-2

a - d = x = 8 - 2 = 6                       a-d = x = 8+2 = 10

a       = y = 8                                    a   = y = 8

a + d = z = 8 + 2 = 10                      a+d = z = 8-2 = 6