Question

The product of two consecutive positive integers is 18 more than eight times the smaller number. Find the two numbers.

Answer 1

Let , smallest integer is x.

So , other one is x + 1.

By , given conditions :

$x( x + 1 ) = 8x + 18\\\\x^2+x=8x+18\\\\x^2-7x-18=0\\\\x^2-9x+2x-18=0\\\\x(x-9)+2(x-9)=0\\\\x=-2 \ ,\ x = 9$

Since, the numbers are positive so, x = -2 is ignored.

Therefore, the numbers are 9 and 10.

Hence, this is the required solution.