Prove :

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- Oct 15th 2009, 01:04 AMdhiabNaturel-number
**Prove :**

- Oct 15th 2009, 02:44 AMred_dog
Let .

Then .

For the right member I'll use the formula . But and

Then .

The only real root, which is also integer is . - Oct 15th 2009, 07:50 AMpacman
Notice that (3 + sqrt 2)^3 = (45 + 29(sqrt 2)),

thus x = [3 + sqrt(2)] + [3 - sqrt (2)] = 3 + 3 = 6.