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

 Jan 22, 2022
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\(x = \)\({1\over2 + {1\over x + 2}}\)

 

This is what the equation looks like, now to simplify:

 

First you multiply the numerator and denominator by (x + 2):

It should look like: x = \({x + 2\over 2x + 4 + 1}\) 

Then you multiply both sides of the equation by \(2x + 5\) to get \(2x^2 + 5x = x + 2\).

Now you subtract (x + 2) from both sides to end up with quadratic: \(2x^2 + 4x - 2 = 0\)

Next you use the quadratic formula x = \(-b {+\over} \sqrt{b^2 - 4ac}\over2a\) where a is the coefficient of x^2, b is the coefficient of x, and c is the constant. Plugging it in, we find that x = \(2\sqrt{2} - 2\), or x = \(-2\sqrt{2} - 2\)

 

 

 

smiley

 Jan 23, 2022

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