# The Product of Two Consecutive Natural Numbers Which Are Multiples of 3 is Equal to 810. Find the Two Numbers. - Mathematics

Sum

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

#### Solution

Let the numbers be 3x, 3 (x +1)
According to question, (3x) × 3( x + 1) = 810

9 [ x^2 + x ] =810

x^2 + x = 90

x^2 + x - 90 = 0

x^2 + 10x -9x - 90 = 0

x ( x + 10) - 9 ( x +10 ) = 0

(x - 9) (x + 10 ) = 0

x = 9 , x = - 10

But x ≠ - 10, because 3x must be natural number .

∴ x = 9

Numbers are 3x, 3 (x  +1 )

⇒ 3 × 9 , 3(9 + 1)

∴ Numbers are ⇒ 27 , 30

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