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decimal expansions fo roots of x\sqrt8 + 1/(x\sqrt8) = \sqrt8 in place 1994

Source: 1994 Swedish Mathematical Competition p1

April 2, 2021
equationalgebraDigit

Problem Statement

x8+1x8=8x\sqrt8 + \frac{1}{x\sqrt8} = \sqrt8 has two real solutions x1,x2x_1, x_2. The decimal expansion of x1x_1 has the digit 66 in place 19941994. What digit does x2x_2 have in place 19941994?
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