<p>If (x + y)^2 - (x - y)^2 = 84 and x and y are positive integers, which of the following could be a value of x + y?</p>
<p>A) 10
B) 12
C) 14
D) 16
E) 18</p>
<p>I have no idea how to approach this. </p>
<p>How would I do this problem?</p>
<p>Thanks in advance!</p>
<p>(x + y)^2 = x^2 +2xy + y^2
(x - y)^2 = x^2 -2xy + y^2
Essentially left with
4xy = 84
xy = 21
x = 3, y = 7, x + y = 10 (A)</p>
<p>well first you expand the polynomial thingies so it’s
(x^2+2xy+y^2)-(x^2-2xy+y^2)=84
and then you simplify to
4xy=84
xy=21
then obviously the only 2 positive values that make 21 is 3 and 7 so
3+7=10</p>
<p>^21 and 1 also make 21 but 22 isnt a solution</p>