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What is the positive solution to the equation x = 1/(2 + 1/(x + 2)) ?

 Jun 28, 2021
 #1
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Multiply the left side by x+2/x+2 to get, \(x=\frac{x+2}{2x+5} \). Multiply both sides by 2x+5,

\(2x^2+5x= x + 2 \)

Subtract x+2 on both sides

\(2x^2+4x-2= 0 \)

Use the quadratic formula to find solutions of, \(x = -1 + \sqrt{2}, -1 - \sqrt{2}\)

We want the positive solution, which is \(-1 + \sqrt{2}\)

 Jun 28, 2021
 #2
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Positive solution: \(x = \sqrt{2}-1\)

 Jun 28, 2021
edited by Guest  Jun 28, 2021

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