Question

Find the value

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Answer 1

For this case we have the following expression:

`3 + 2 \sqrt {2} + \frac {1} {3 + 2 \sqrt {2}} =`

We rationalize the second term multiplying by:

`\frac {3-2 \sqrt {2}} {3-2 \sqrt {2}}:`
`\frac {1} {3 + 2 \sqrt {2}} * \frac {3-2 \sqrt {2}} {3-2 \sqrt {2}} = \frac {3-2 \sqrt {2} } {9-6 \sqrt {2} +6 \sqrt {2} -4 (\sqrt {2}) ^ 2} = \frac {3-2 \sqrt {2}} {9-4 * 2} = \frac {3-2 \sqrt {2}} {1} = 3-2 \sqrt {2}`

So, we have:

`3 + 2 \sqrt {2} + 3-2 \sqrt {2} = 3 + 3 = 6`

Answer:

6