SOLUTION: If a>0 and b>0, a+b = t, show that {{{1/a + 1/b >= 4/t }}}

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Question 1184376: If a>0 and b>0, a+b = t, show that 1%2Fa+%2B+1%2Fb+%3E=+4%2Ft+
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


If you prefer, you can reverse the 
steps and omit the "if and only If"'s.

Edwin

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The statement follows almost immediately from the AM-HM inequality:
Since a,b > 0, then %28a%2Bb%29%2F2+%3E=+2%2F%281%2Fa+%2B+1%2Fb%29

===> 1%2Fa+%2B+1%2Fb+%3E=+4%2F%28a%2Bb%29+=+4%2Ft.