Q. 4 B

Sum of three numbers in A.P. is 3 and their product is — 35. Find the numbers.

Answer :

Let the three numbers are (a – d), a and (a + d)


According to question,


Sum of these three numbers = 3


a – d + a + a + d = 3


3a = 3


a = 1 …(i)


and it is also given that


Product of these numbers = – 35


(a – d) × a × (a + d) = – 35


(1 – d) × 1 × (1 + d) = – 35


1 × (12 – d2) = – 35 [ (a – b)(a + b) = a2 – b2]


1 × (1 – d2) = – 35


1 – d2 = – 35


– d2 = – 35 – 1


– d2 = – 36


d2 = 36


d = √36


d = ±6


Case I: If d = 6 and a = 1


a – d = 1 – 6 = – 5


a = 1


a + d = 1 + 6 = 7


So, the numbers are


– 5, 1, 7


Case II: If d = – 6 and a = 1


a – d = 1 – ( – 6) = 1 + 6 = 7


a = 1


a + d = 1 + ( – 6) = 1 – 6 = – 5


So, the numbers are


7, 1, – 5


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