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Question Number 12197 by tawa last updated on 16/Apr/17

Commented by mrW1 last updated on 16/Apr/17

$$Ithinkwecannotfindananalytical$$$$solution.Thenumericalsolutioncan$$$$befoundusingalotofapps,e.g.geogebra.$$$$x\approx 2.76909366$$

Commented by mrW1 last updated on 16/Apr/17

$$analyticalsolutioncanbefoundfor$$$$5-x=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}$$$$whichisx=5-\sqrt{5}$$

Commented by tawa last updated on 16/Apr/17

$$\mathrm{x}=2.7690.....$$$$\mathrm{i}\mathrm{need}\mathrm{a}\mathrm{workings}\mathrm{to}\mathrm{the}\mathrm{correct}\mathrm{answer}.$$

Commented by tawa last updated on 16/Apr/17

$$\mathrm{please}\mathrm{sir},\mathrm{can}\mathrm{you}\mathrm{show}\mathrm{me}\mathrm{the}\mathrm{workings}...\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by tawa last updated on 16/Apr/17

$$\mathrm{please}\mathrm{sir}!$$

Commented by mrW1 last updated on 16/Apr/17

$$a-x=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}$$$$a=x+\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}$$$$\Rightarrow a=x+\sqrt{a}$$$$\Rightarrow x=a-\sqrt{a}$$$$$$$$fora=5$$$$x=5-\sqrt{5}$$

Commented by tawa last updated on 16/Apr/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$$$\mathrm{But}\mathrm{how}\mathrm{is}\mathrm{a}=5...$$$$\mathrm{Is}\mathrm{it}\mathrm{trial}\mathrm{and}\mathrm{error}\mathrm{method}?$$

Commented by tawa last updated on 16/Apr/17

$$\mathrm{ohhh},\mathrm{i}\mathrm{have}\mathrm{seen}\mathrm{it}\mathrm{sir}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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