The sum of three numbers in A.P. is -3. and their product in 8. Find the numbers. [ncert]

The sum of three numbers in A.P. is -3. and their product in 8. Find the numbers.

Let the three numbers are a-d, a and a+d. Here a is the first term and d  the Common difference.

Now given that (a - d) + a + (a + d) = - 3

=> 3a = - 3 => a = - 1

Now (a - d) * a* (a + d) = 8

=> a(a - d)(a + d) = 8 => a(a² - d²) = 8 

 => (-1){(-1)²-d²)}=8

=> (-1)(1-d²)=8 => -1+d²=8

=> d²=9 => d=±3

Now take a = - 1 and d = 3 

=> a-d, a, a+d= -1-3, -1, -1+3 = -4,-1,2 Ans.

Now take a= -1 and d= -3, then a-d, a, a+d becomes, -1-(-3), -3, -1+(-3)

= 2, -3, -4. Ans.