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April 3rd, 2014, 12:11 PM   #1
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a and b

(1+ root(2) )^2006=a+broot(2)
find a^2-2b^2
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April 3rd, 2014, 12:36 PM   #2
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This problem is outdated: it is from 2006. Next, please!

Seriously, note that $\displaystyle a^2-2b^2=(a+\sqrt{2}b)(a-\sqrt{2}b)$ and try expressing $\displaystyle a-\sqrt{2}b$ similarly to how $\displaystyle a+\sqrt{2}b$ is defined.
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