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Question Number 169727 by Mastermind last updated on 07/May/22

Commented by Mastermind last updated on 07/May/22

$$Okay,thanks$$

Commented by mr W last updated on 07/May/22

$$youcanexpressanynaturalnumber$$$$inthisway$$$$n=\sqrt{n(n-1)+\sqrt{n(n-1)+\sqrt{n(n-1)+...}}}$$

Commented by cortano1 last updated on 07/May/22

$$\sqrt{42+\sqrt{42+\sqrt{42+\sqrt{42+\sqrt{...}}}}}=x$$$$42+x=x^2$$$$\Rightarrow x^2-x-42=0$$$$\Rightarrow (x-7)(x+6)=0$$$$\Rightarrow x=7;x=-6\left(rejected\right)$$

Commented by Mastermind last updated on 07/May/22

$$yoursolution@mrW$$

Commented by mr W last updated on 07/May/22

$$n=\sqrt{m+\sqrt{m+\sqrt{m+...}}}$$$$n=\sqrt{m+n}$$$$n^2=m+n$$$$\Rightarrow m=n^2-n=n(n-1)$$$$\Rightarrow n=\sqrt{n(n-1)+\sqrt{n(n-1)+\sqrt{n(n-1)+...}}}$$

Commented by Mastermind last updated on 07/May/22

$$Thanks$$

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