Value of x that satisfies relation x = 1 - x + x^2 - x^3 + x^4 - x^5 + ......... ∞

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3.Trigonometrical Ratios, Functions and Identities

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The value of $x$ that satisfies the relation $x = 1 - x + x^2 - x^3 + x^4 - x^5 + ......... \infty$

A

$2\, cos36^°$

B

$2 \,cos144^°$

C

$2\, sin18^°$

D

none

Solution

$x = \frac{1}{{1 + x}}$ $\Rightarrow$ $x^2 + x – 1 = 0$

$x = \frac{{ – 1 + \sqrt 5 }}{2}$ or $\frac{{ – 1 – \sqrt 5 }}{2}$ (rejected, think ! )

hence $x = \left( {\frac{{\sqrt 5 – 1}}{4}} \right)\,\cdot\,2 = 2 \, sin18^°$

Standard 11

Mathematics

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