13which one does not hold????
x,y,z real show that
mod(x)+mod(y)+mod(z) ≤ mod(x+y-z) + mod(y+z-x) + mod(z+x-y)
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8 Answers
13bhaiya...why did u rite...
|x|+|y|+|z|<2x+|y+z-x|
62wlog assume
x>y>z
so |x+y-z| = x+y-z and
|x+z-y|=x+z-y
|x|+|y|+|z|
|x|+|y|+|z|<2x+|y+z-x|
if y+z-x>0 then
|x|+|y|+|z|<2x+y+z-x = x+y+z which is not true
try x=6, y=5 and z=5
this does not hold
341|x| = 1/2 |(x+y-z) + (x+z-y)| ≤ 1/2 |x+y-z| + 1/2 |x+z-y|
and two similar inequalities with y and z, adding which gives you the required inequality
