What is the numerical value of x = \(\frac{1}{4-\frac{1}{4-\frac{1}{4-\ldots}}} \)?
+2666 We have the equation: \(x = {1 \over { 4 - x}}\).
Multiplying both sides by \(4 - x\) gives us: \(-x^2 + 4 x = 1\).
Subtracting 1 from both sides gives us: \(-x^2 + 4x - 1 = 0 \)
Using the quadratic formula, we find \(x = \color{brown}\boxed{2 \pm \sqrt 3}\)
+2666 We have the equation: \(x = {1 \over { 4 - x}}\).
Multiplying both sides by \(4 - x\) gives us: \(-x^2 + 4 x = 1\).
Subtracting 1 from both sides gives us: \(-x^2 + 4x - 1 = 0 \)
Using the quadratic formula, we find \(x = \color{brown}\boxed{2 \pm \sqrt 3}\)
