1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Simplyfiying y^2 = x^2

  1. Mar 6, 2017 #1
    Say we have that ##y^2 = x^2##. Then if we take the square root of both sides, it would seem that we have ##|y| = |x|##. Why does this imply that that ##y=x## or ##y=-x##, rather than implying that ##y=|x|## or ##y=- |x|##?
  2. jcsd
  3. Mar 6, 2017 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    The two answers are equivalent.

    We agree that a = |x| means that
    a = x or
    a = -x.

    If you let a = |y| then
    (1) |y| = x or
    (2) |y| = -x

    But (1) x = |y| means x = y or x = -y and (2) -x = |y| means -x = y or -x = -y (i.e. x = y). So, y = x or y = -x.

  4. Mar 7, 2017 #3


    Staff: Mentor

    Why not just do this?
    ##y^2 = x^2 \Leftrightarrow y^2 - x^2 = 0 \Leftrightarrow (y - x)(y + x) = 0 \Leftrightarrow y = x \text{ or } y = -x##
  5. Mar 7, 2017 #4


    User Avatar
    2017 Award

    Staff: Mentor

    Yet another approach:
    If |x|=|y|, there are four cases:
    x and y positive: then x=y
    x positive, y negative: x=-y
    x negative, y positive: x=-y
    x and y negative: x=y
    Combined, x=y or x=-y. In other words, the two variables are identical up to a possible difference in their sign.

    I neglected the option x=y=0 here, but that fits to the answer as well.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted