Question

the sum of three term of an AP is -3 and their product is 8. find the number​

Answer 1

Answer :

2 , -1 , -4

Solution :

Let the three terms in AP be ;

(a - d) , a , (a + d) .

Now ,

According to the question , the sum of the three terms in AP is -3 .

Thus ,

=> (a - d) + a + (a + d) = -3

=> 3a = -3

=> a = -3/3

=> a = -1

Also ,

The product of the three terms in AP is 8 .

Thus ,

=> (a - d)•a•(a + d) = 8

=> a•(a² - d²) = 8

=> -1•[ (-1)² - d² ] = 8

=> -1•(1 - d²) = 8

=> d² - 1 = 8

=> d² = 8 + 1

=> d² = 9

=> d = √9

=> d = ± 3

Case 1 : If a = -1 and d = 3

1st no. = a - d = -1 - 3 = -4

2nd no. = a = -1

3rd no. = a + d = -1 + 3 = 2

Case 2 : If a = -1 and d = -3

1st no. = a - d = -1 - (-3) = -1 + 3 = 2

2nd no. = a = -1

3rd no. = a + d = -1 + (-3) = -1 - 3 = -4

Hence ,

Required numbers are : 2 , -1 , -4