Question

⭐Sum of 3 numbers is 3 and the product is - 35.Find the numbers.⭐

CLASS 10 CHAPTER :ARITHMETIC PROGRESSIONS

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Answer 1

let three numbers be a, a-d ,a+d
now
according to the question
a+a-d+a+d=3
=> a=1
also a(a-d)(a+d)=-35
a(a²-d²)=-35
putting a =1
1(1-d²)=-35
=> d=±6
putting a and d in very first step
so numbers are
1 , 7 , -5

Answer 2

Let the numbers be a - d, a, a + d.

Given that sum of 3 numbers is 3.

⇒ a - d + a + a + d = 3.

⇒ 3a = 3

⇒ a = 1.

Given that Product of three numbers is -35.

⇒ (a - d) * a * (a + d) = -35

⇒ a * (a^2 - d^2) = -35

⇒ a^2 - d^2 = -35

⇒ 1 -d^2 = -35

⇒ -d^2 = -36

⇒ d = 6,-6.

When a = 1 and d = 6:

⇒ a = 1

⇒ a - d = -5

⇒ a + d = 7.

When a = 1 and d = -6:

⇒ a = 1

⇒ a - d = 1 + 6 = 7

⇒ a + d = -5.

Therefore, the numbers are 1,-5,7.

Hope this helps!