Question

'Word Problems Involving Products and Factoring'

Find two consecutive positive numbers such that the product of the sum and difference of the numbers plus 8 is the sum of their squares.

Answer 1

`x,x+1- two\ consecutive\ numbers\\\\ Condition:\\x>0\ and\ x+1>0\\x>0\ and\ x>-1\\\\ (x+x+1)(x+1-x)+8=x^2+(x+1)^2\\\\(2x+1)*1+8=x^2+x^2+2x+1\\\\2x+1+8=2x^2+2x+1\\\\-2x^2+2x-2x=1-8-1\\\\-2x^2=-8\ \ |:(-2)\\\\x^2=4\\\\x=2\ \ or\ \ x=-2\ -\ reject\ conditions\ are\ not\ satisfied\\\\Two\ consecutive\ numbers\ are:\ 2\ and\ 3.`