Answered

Get detailed and accurate responses to your questions with IDNLearn.com. Discover prompt and accurate answers from our community of experienced professionals.

'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.

Sagot :

Luanaidn
[tex]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. [/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.