Modulus and Algebra: Combined!

Algebra Level 3

$x$ and $y$ are 2 distinct real numbers. Given that $|x-y|$ $|y-x|$ $-$ $(x+y)^2$ $= 28,$ find the value of $xy.$

1 solution

Winston Choo
Apr 12, 2020

The important step to solving this problem is knowing that $|x - y|$ $=$ $| -$ $(y-x)|$ $=$ $|y - x|$ . Now,

$|x-y|$ $|y-x|$ $- (x+y)^2$ $=28$

$|x-y|$ $|x-y|$ $- (x+y)^2$ $=28$

$|x-y|^2$ $- (x+y)^2$ $=28$

$(x-y)^2$ $- (x+y)^2$ $=28$

$(x^2 - 2xy + y^2)$ $- (x^2 + 2xy + y^2)$ $=28$

$-4xy$ $=28$

$xy$ $=-7$