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Question
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Solution
Let the required numbers be (a - d ),a and (a +d).
Then (a-d) +a +(a+d) = 3
⇒ 3a = 3
⇒ a = 1
Also , (a- d) .a . (a +d) = -35
⇒ a,`(a^2 - d^2 ) = -35`
⇒ 1.`(1-d^2 ) =-35`
⇒ `d^2 = 36 `
⇒ `d = +- 6`
Thus , a = 1 and d = `+-6`
Hence, the required numbers are (-5 ,1 and 7 ) or (7,1 and -5)
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