Below the lines infinity

Algebra Level 1

2 x x 2 + 2 x x 2 + 2 x x 2 + 2 x x 2 + . . . = 1 , x = ? \large \frac { \color{#20A900}{2x} }{ { \color{#3D99F6}{x^2} }+\frac { \color{#20A900}{2x} }{ { \color{#3D99F6}{x^2} }+\frac { \color{#20A900}{2x} }{ { \color{#3D99F6}{x^2} }+\frac { \color{#20A900}{2x} }{ \color{#3D99F6}{x^2}+... } } } } = \color{#624F41}1, \ \ \ \ \ \ \ \ x = \ ?


The answer is 1.

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Edgar de Asis Jr. by Edgar de Asis Jr. , 25, Philippines

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2 solutions

Alex Zhong
Mar 31, 2015

The equation is simplified as

2 x x 2 + 1 = 1 ⟹ x 2 − 2 x + 1 = 0 ⟹ x = 1 . \dfrac{2x}{x^2+1} = 1 \implies x^2-2x+1 = 0 \implies x=\boxed{1}.

7 Helpful 0 Interesting 2 Brilliant 0 Confused

Rest of the answer is given by Alex Zhong

4 Helpful 0 Interesting 1 Brilliant 0 Confused

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