X Is A Negative Number, Really?

Algebra Level 2

x x + x x + x x + x x + . . . = 2 \large{\dfrac{x}{x + \dfrac{x}{x + \dfrac{x}{x + \dfrac{x}{x + ...}}}} = 2}

Find the value of x x that satisfy the equation above


The answer is -4.

Muhammad Rizki Fadillah by Muhammad Rizki Fadillah , 31, Indonesia

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1 solution

x x + x x + x x + x x + . . . = 2 \large{\dfrac{x}{x + \dfrac{x}{x + \dfrac{x}{x + \dfrac{x}{x + ...}}}} = 2}

The infinity fraction value is 2, so

x x + 2 = 2 \large{\dfrac{x}{x + 2} = 2}

Simply move x + 2 x + 2 to the right side

x = 2 ( x + 2 ) x = 2(x + 2)

x = 2 x + 4 x = 2x + 4

x = − 4 x = \boxed{-4}

*cmiiw

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