#### Question

Find the two consecutive natural numbers whose product is 20.

#### Solution

Let the two consecutive natural numbers be ‘x’ and ‘x + 2’

⇒ Given that the product of the natural numbers is 20

Hence ⇒ x(x + 1) = 20

⇒ 𝑥^{2} + 𝑥 = 20

⇒ 𝑥^{2} + 𝑥 - 20 = 0

⇒ 𝑥^{2} + 5𝑥 - 4𝑥 - 20 = 0

⇒ 𝑥(𝑥 + 5) - 4(𝑥 + 5) = 0

⇒ 𝑥 = -5 𝑜𝑟 𝑥 = 4

Considering positive value of x as x ∈ N

For r = 4, x + 1 = 4 + 1 = 5

∴ The two consecutive natural numbers are 4 as 5.

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#### APPEARS IN

Solution Find the Two Consecutive Natural Numbers Whose Product is 20. Concept: Solutions of Quadratic Equations by Factorization.