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# Algebra

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

Jan 22, 2022

#1
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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 = $$-2\sqrt{2} - 2$$

Jan 23, 2022