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Find positive integers (a,b) so that

(37 + 20*sqrt(3))^2 = a + b*sqrt(3).

 Jul 5, 2022
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Find positive integers (a,b) so that:

\((37+20\sqrt{3})^2=a+b\sqrt{3}\)
Expanding the L.H.S:

\(1369+1480\sqrt{3}+1200=a+b\sqrt{3}\)

\(2569+1480\sqrt{3}=a+b\sqrt{3}\)

So it must follow that, by comparing coefficients: 

\(a=1369+1200=2569\)

\(b=1480\)

Hope this helps!

 Jul 5, 2022

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