One of the basic question from arithmetic progression chapter in which we are to find the numbers, if their product is -35 and their sum is 3.
RS Aggarwal, class 10, chapter 5B, question no 7
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
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Let a−d,a,a+d are three numbers in AP.
Their sum=a−d+a+a+d=3
3a=3
or a=1
Again,
Their Product=(a−d)×a×(a+d)=−35
a(a^2−d^2)=−35
(1^2−d^2)=−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.