Question

The product of two successive numbers is 8556. Which is the smallest number?

Answer 1

Let a and a+1 are the two successive numbers with ‘a’ being the smaller.

Given a × (a + 1) = 8556

⇒ a2 + a – 8556 = 0

This is a quadratic equation in variable a

⇒ a2 + 93a – 92a – 8556 = 0

⇒ a(a+93) – 92(a+93) = 0

⇒ (a – 92) (a + 93) = 0

⇒ a = 92

∴ The smaller number = a = 92

Answer 2

Answer:

Explanation:

Let x and x+1 are the two successive numbers with ‘x" being the small

Given x × (x + 1) = 8556

⇒ x2 + x – 8556 = 0

This is a quadratic equation in variable x

⇒ x2 + 93x – 92x – 8556 = 0

⇒ x(x+93) – 92(x+93) = 0

⇒ (x – 92) (x + 93) = 0

⇒ x = 92

∴ The smallest number = x = 92