An algebra problem by Sumukh Bansal

Algebra Level 2

Let $x$ and $y$ be numbers satisfying $x = \dfrac1{1+x}$ and $y = \dfrac1{1 + \frac1{1+y}}$ , what is the integer value of $|x-y |$ ?

Notation: $| \cdot |$ denotes the absolute value function .

The answer is 0.

1 solution

Chew-Seong Cheong
Sep 16, 2017

$\begin{aligned} y & = \frac 1{1+\color{#3D99F6}\frac 1{1+y}} & \small \color{#3D99F6} \text{Note that }x = \frac 1{1+x} \\ & = \frac 1{1+\color{#3D99F6}y} \\ \implies y & = x \\ \implies |x - y| & = \boxed{0} \end{aligned}$

An algebra problem by Sumukh Bansal

The answer is 0.

1 solution

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