Question

Prove that for every two positive integers a and b that

\((a+b)(\frac{1}{a}+\frac{1}{b}) > or = 4\)

Answer 1

`\((a+b)((1)/(a)+(1)/(b)) \ \textgreater \ or = 4\) \\ 1+a/b+b/a + 1 \geq 4`
`\((a+b)((1)/(a)+(1)/(b)) \ \textgreater \ or = 4\)`

distributed

choose 1 as your lowest positive integer

plug 1 into a and b

1 + 1 + 1 + 1
`\geq 4`