Question

Three numbers are in Ap. If the sum of these numbers is 27 and the product is 648 find the numbers

Answer 1

Hope it is helpful:-)

Answer 2

Answer:

6,9,12 Or 12,9,6 are required

three terms in A.P

Explanation:

Let (a-d), a , (a+d) are three terms in A.P

i ) sum of three terms =27

[given]

=> a-d+a+a+d = 27

=> 3a = 27

=> a = 27/3

=> a = 9 -------(1)

ii) The product of three terms = 648 [ given ]

=> (a-d)×a×(a+d) = 648

=> (a²-d²)a = 648

=> (9² - d²)×9 = 648 [ from (1)]

=> 81 - d² = 648/9

=> 81 - d² = 72

=> -d² = 72 - 81

=> -d² = -9

=> d² = 3²

=> d = ±√3²

=> d = ±3

Therefore,

case1:

If a = 9, d = 3

a-d = 9-3 = 6

a = 9

a+d = 9+3 = 12

Required three terms = 6,9,12

case 2:

If a = 9, d = -3

a-d = 9 -(-3) = 9+3 = 12

a = 9

a+d = 9+(-3) = 9-3 = 6

Required three terms = 12,9,6

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