Question

The sum of four integers in AP is 24 and their product is 945. Find the numbers.

Answer 1

4 numbers in AP are taken as a-3d,a-d,a+d,a+3d
their sum is = a-3d+a-d+a+d+a+3d= 4a
4a = 24 (given)
a =6
(6-3d)(6-d)(6+d)(6+3d) = 945
3(2-d)(36-d^2)3(2+d) = 945
9 (4-d^2)(36-d^2)= 945
(4-d^2)((36-d^2)= 105
144 -40d^2+ d^4 = 105
d^4-40d^2+39=0
(d^2-39)(d^2-1)=0
d =sqrt(39 cannot be as numbers are integers
so d = +1 and d=-1
So numbers are
for d =1 , (6-3(1)) ,( 6-1), (6+1),(6+3(1))
= 3,5,7,9
for d =-1, (6-3(-1)),(6-(-1),(6-1),(6+3(-1)
9 , 7 , 5 ,3
Numbers are same 3,5,7,9