Solve... $5 - x = sqrt(x + sqrt(x + sqrt(x + sqrtx)))$ Find $x$ ?

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Answer 1 · 2017-11-22T09:22:21

The answer is $=5-sqrt5$

Let $y=sqrt(x+sqrt(x+sqrt(x+sqrt(x+....))))$

Squaring,

$y^2=x+sqrt(x+sqrt(x+sqrt(x+sqrt(x+....))))$

$y^2=x+y$

As,

$y=5-x$

$y^2=x+5-x=5$

$y=+-sqrt5$

Therefore,

$y^2=x+y$

$5=x+sqrt5$

$x=5-sqrt5$

Solve... 5 - x = sqrt(x + sqrt(x + sqrt(x + sqrtx)))5 - x = sqrt(x + sqrt(x + sqrt(x + sqrtx))) Find xx?