SOLUTION: If x>0,y>0,z>0 and x+y+z=1,prove that {{{x/2-x + y/2-y + z/2-z>=3/5}}}

Algebra ->  Sequences-and-series -> SOLUTION: If x>0,y>0,z>0 and x+y+z=1,prove that {{{x/2-x + y/2-y + z/2-z>=3/5}}}      Log On


   

Question 51695: If x>0,y>0,z>0 and x+y+z=1,prove that x%2F2-x+%2B+y%2F2-y+%2B+z%2F2-z%3E=3%2F5
Answer by darq(90) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F2-x+%2B+y%2F2-y+%2B+z%2F2-z+%3E=3%2F5

-x%2F2-y%2F2-z%2F2+%3E=+3%2F5

after multiplying both sides with -2. we will need to change sides because it is negative.
-6%2F5+%3E=+x%2By%2Bz

-6%2F5+%3E=+1

a positive number is always bigger than a negative so 1 is bigger than -6%2F5. So it is proven that equation is in fact WRONG. But if you had written > instead of < of course the equation will be correct or if you had forgotten to put (-) before 5%2F3 it would have been correct.