The difference between 2 integers is four, and the sum of two integers is sixteen. What is the absolute value of the difference of the squares of the integers?

Okay, ALL I can think of for this is guess and check. Is there a smarter method, and how?

tommarvoloriddle Nov 10, 2019

#2**+1 **

Hi Tom..riddle

The difference between 2 integers is four, and the sum of two integers is sixteen. What is the absolute value of the difference of the squares of the integers?

\(|x-y|=4 \qquad x+y=16 \qquad find\;\;|x^2-y^2|\\~\\ (x-y)^2=16\\ x^2+y^2-2xy=16\;\;(1)\\~\\ x+y=16\\ x^2+y^2+2xy=256\;\;(2)\\~\\ (2)-(1)\\ 4xy=240\\ xy=60 \)

So the 2 integers add to 16 and multiply to 60

You can take it from there.

Melody Nov 10, 2019