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Question

The sum of three numbers in AP is 3 and their product is 35. Find the numbers.

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Solution

Let ad,a,a+d are three numbers in AP.
Their sum=ad+a+a+d=3
3a=3
or a=1
Again,
Their Product=(ad)×a×(a+d)=35
a(a2d2)=35
(12d2)=35
or d=±6
d=6 or d=6
We have 2 conditions here:
At a=1,d=6
Numbers are: 5,1 and 7
At a=1 and d=6
Numbers are: 7,1,5.

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