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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?

 Nov 10, 2019
 #1
avatar+1692 
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reposted.

 Nov 10, 2019
 #2
avatar+106981 
+1

 

Hi Tom..riddle  laugh

 

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.

 Nov 10, 2019
 #3
avatar+2551 
+1

Satisfying solution by Melody here!

CalculatorUser  Nov 10, 2019

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