emster128
emster128 emster128
  • 02-03-2017
  • Mathematics
contestada

Prove that for every two positive integers a and b that
\((a+b)(\frac{1}{a}+\frac{1}{b}) > or = 4\)

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  • 02-03-2017
[tex]\((a+b)(\frac{1}{a}+\frac{1}{b}) \ \textgreater \ or = 4\) \\ 1+a/b+b/a + 1 \geq 4 [/tex][tex]\((a+b)(\frac{1}{a}+\frac{1}{b}) \ \textgreater \ or = 4\) [/tex]

distributed 

choose 1 as your lowest positive integer

plug 1 into a and b

1 + 1 + 1 + 1[tex] \geq 4[/tex]

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