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What is the numerical value of x = \(\frac{1}{4-\frac{1}{4-\frac{1}{4-\ldots}}} \)?

 Jun 22, 2022

Best Answer 

 #1
avatar+2222 
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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 \(x = \color{brown}\boxed{2 \pm \sqrt 3}\)

 Jun 23, 2022
 #1
avatar+2222 
+1
Best Answer

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 \(x = \color{brown}\boxed{2 \pm \sqrt 3}\)

BuilderBoi Jun 23, 2022

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