Question

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Answer 1

Answer:

The three numbers are 6, 9, 12.

Step-by-step explanation:

Given :

Sum of three numbers be 27.

Let the three numbers in AP are (a – d), a, (a + d)

Then, we have,

(a – d) + a + (a + d) = 27

3a = 27

a = 27/3

a = 9 …………..(1)

Also it is given that the product of three numbers be 648, therefore we have,  

(a – d) (a) (a + d) = 648

(a²– d²) (a) = 648

(9² – d²) 9 = 648

[From eq 1 , a = 9]

(81 – d²) = 648/9

(81 – d²) = 72

d² = 81 - 72

d² = 9

d = 3

Therefore, (a – d) = 9 – 3 = 6

(a + d) = 9 + 3 = 12

Hence, the three numbers are 6, 9, 12.

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Answer 2

Step-by-step explanation:

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