The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.
Quadratic Equations
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Question

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

KnowledgeBoat · Accepted Answer

Given, Let two consecutive natural numbers multiple of 3 be 3n and 3n + 3. Given, The product is 810. ⇒ 3n(3n + 3) = 810 ⇒ n(3n + 3) = ⇒ 3n2 + 3n = 270 ⇒ 3n2 + 3n - 270 = 0 ⇒ 3(n2 + n - 90) = 0 ⇒ n2 + n - 90 = 0 ⇒ n2 + 10n - 9n - 90 = 0 ⇒ n(n + 10) - 9(n + 10) = 0 ⇒ (n - 9)(n + 10) = 0 ⇒ (n - 9) = 0 or (n + 10) = 0 [Using zero-product rule] ⇒ n = 9 or n = -10. n = 9 [Since the numbers are natural numbers] First multiple is 3n = 3(9) = 27 Second multiple is 3n + 3 = 3(9) + 3 = 27 + 3 = 30. Hence, two consecutive natural multiples of 3 are 27 and 30.

Mathematics

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

Quadratic Equations

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