Q. 64.0( 19 Votes )

Find three numbers in AP whose sum is 15 and product is 80.

Answer :

Let the numbers be (a - d), a, (a + d).

Now, sum of the numbers = 15


(a - d) + a + (a + d) = 15


3a = 15


a = 5


Now, product of the numbers = 80


(a - d) × a × (a + d) = 80


a3 - ad2 = 80


Put the value of a, we get,


125 - 5 d2 = 80


5 d2 = 125 - 80 = 45


d2 = 9


d = � 3


If d = 3, then the numbers are 2, 5, 8.


If d = - 3, then the numbers are 8, 5, 2.


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