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\[\sqrt{a^2+b^2}x = a_0 + \frac{1}x = a_0 + \frac{1}{\displaystyle a_1 + \frac{1}{\displaystyle a_2 + \frac{1}{\displaystyle a_3 + a_4}}}{a_1 + \frac{1}{a_2 + \frac{1}{a_3 + a_4}}}\]