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# MATTTTTHHHHHCCCCCOOOOOUUUUUNNNNNTTTTTSSSSS

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81
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+1692

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
+1692
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reposted.

Nov 10, 2019
#2
+106981
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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.

Nov 10, 2019
#3
+2551
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Satisfying solution by Melody here!

CalculatorUser  Nov 10, 2019