1. ## Root problem

Find x:
x = sq.root[1 + sq.root( 1 + sq.root(1 + sq.root(1 +....
"The dots mean that the series go till infinity.
By attempt the answer should be (1 +-sq.root(5))/2 but that is not the answer.

2. ## Re: Root problem

/the answer is $\displaystyle \frac{1 \frac{+}{-} \sqrt(5)}{2}$

The infinite nested radicals, $\displaystyle \sqrt(1 + \sqrt(1 + \sqrt(1 + ....$ = golden ratio.

Since golden ratio says $\displaystyle \frac{a+b}{a} = \frac{a}{b} = x$ then $\displaystyle 1 + \frac{b}{a} = 1 + \frac{1}{x} = x$ so solving $\displaystyle x^2 - x - 1 = 0$

3. ## Re: Root problem

Could you please write as to what is the answer given. The answer you have got appears to be correct.

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5. ## Re: Root problem

$\displaystyle \text{Evaluate: }\:x \:=\: \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}$
By attempt the answer should be: $\displaystyle \frac{1\pm\sqrt{5}}{2}$, but that is not the answer.
Since $\displaystyle x$ is obviously positive,
. . you must reject the negative root: $\displaystyle \tfrac{1-\sqrt{5}}{2}$