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- 1 month ago
sqrt(2) = 1 + 1 / (2 + 1 / (2 + 1 / (2 + .....

sqrt(3) = 1 + 1 / (1 + 1 / (2 + 1 / (1 + 1 / (2 + 1 / (....

sqrt(2)Xsqrt(3) = 1 + 1 + 1 / (2 + 1 + 1 / (2 + 2 + 1 / (2 + 1 + 1 / (....

sqrt(2)Xsqrt(3) = k

k = 2 + 1 / (3 + 1 / (4 + 1 / (3 + 1 / (....

k - 2 = 1 / (3 + 1 / (4 + 1 / (3 + 1 / (....

k - 2 = 1 / (3 + 1 / (4 + k - 2))

k - 2 = 1 / (3 + 1 / (2 + k))

k - 2 = 1 / ((3 * (k + 2) + 1) / (k + 2))

(k - 2) = (k + 2) / (3k + 6 + 1)

(k - 2) * (3k + 7) = k + 2

3k^2 - 6k + 7k - 14 = k + 2

3k^2 + k - 14 = k + 2

3k^2 = 16

k^2 = 16 / 3

16 + 3 = 19

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