Question

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

Answer 1

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