An important question from ML Agarwal of Class10 for board examination We have asked The sum of the three numbers in AP is 3 and their products is -35. Find the numbers.
ML Publication, Class 10, Arithmetic Progression Chapter 9 question no 22
The sum of the three numbers in AP is 3 and their products is -35. Find the numbers.
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Let three no’s in AP be a−d,a,a+d
Given, sum of three numbers =−3
Therefore, a−d+a+a+d=−3
⇒3a=−3
⇒a=−1
Also product of three numbers =8
Therefore, (a−d)a(a+d)=8
⇒a(a2−d2)=8
⇒(−1)(1−d2)=8
⇒1−d2=−8
⇒d2=9
⇒d=3 and d=−3
If a=−1 and d=3
numbers are −4,−1,2.
And if a=−1 and d=−3
numbers are 2,−1,−4.