Q. 105.0( 1 Vote )

# Three numbers are in A.P. If the sum of these numbers be 27 and the product648, find the numbers.

Given:

Sum = 27

Product = 648

Let the three numbers be a – d, a, a+ d.
Therefore,

a – d + a + a + d = 27
3a = 27
a = 9
And,

(a – d)(a)(a + d) = 648
a(a 2 – d 2 ) = 648
9(9 2 – d 2 ) = 648                                   [ a = 9]
9 2 – d 2 = 72
d 2 = 81 - 72
d 2 = 9
d = 3
Hence, The numbers are 6, 9, 12.

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