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Inequality show that question involving two equations

  1. Mar 25, 2013 #1
    Hi, so here is my question that I am totally stumped on.

    for all real values of x and y, show that |x|+|y|≥ √(x^2+y^2 )

    and find the real values of x and y in which equality holds.


    I sorta thought I could do the second part, but it confuses me with two pronumerals and how to get rid of one so that I can find the other.
     
  2. jcsd
  3. Mar 25, 2013 #2
    Both sides are positive so the inequality must hold if and only if the square of both sides satisfies the same inequality. That might simplify it a bit.
     
  4. Apr 7, 2013 #3
    |x| + |y| ≥ √(x*x +y*y) / ( )2 squaring

    x*x + y*y + 2*|x*y| ≥ x*x + y*y /-x*x,-y*y

    2*|x*y| ≥ 0 /:2

    |x*y| ≥ 0 It is true.


    |x*y| = 0 ↔ x = 0 or y = 0

    kamke
     
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