Question Number 12197 by tawa last updated on 16/Apr/17
Commented by mrW1 last updated on 16/Apr/17
$${I}\:{think}\:{we}\:{can}\:{not}\:{find}\:{an}\:{analytical} \\ $$$${solution}.\:{The}\:{numerical}\:{solution}\:{can} \\ $$$${be}\:{found}\:{using}\:{a}\:{lot}\:{of}\:{apps},\:{e}.{g}.\:{geogebra}. \\ $$$${x}\approx\mathrm{2}.\mathrm{76909366} \\ $$
Commented by mrW1 last updated on 16/Apr/17
$${analytical}\:{solution}\:{can}\:{be}\:{found}\:{for} \\ $$$$\mathrm{5}−{x}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+...}}}} \\ $$$${which}\:{is}\:{x}=\mathrm{5}−\sqrt{\mathrm{5}} \\ $$
Commented by tawa last updated on 16/Apr/17
$$\mathrm{x}\:=\:\mathrm{2}.\mathrm{7690}..... \\ $$$$\mathrm{i}\:\mathrm{need}\:\mathrm{a}\:\mathrm{workings}\:\mathrm{to}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{answer}. \\ $$
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
$${a}−{x}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+...}}}} \\ $$$${a}={x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+...}}}} \\ $$$$\Rightarrow{a}={x}+\sqrt{{a}} \\ $$$$\Rightarrow{x}={a}−\sqrt{{a}} \\ $$$$ \\ $$$${for}\:{a}=\mathrm{5} \\ $$$${x}=\mathrm{5}−\sqrt{\mathrm{5}} \\ $$
Commented by tawa last updated on 16/Apr/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\: \\ $$$$\mathrm{But}\:\mathrm{how}\:\mathrm{is}\:\mathrm{a}\:=\:\mathrm{5}... \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{trial}\:\mathrm{and}\:\mathrm{error}\:\mathrm{method}\:? \\ $$
Commented by tawa last updated on 16/Apr/17
$$\mathrm{ohhh},\:\mathrm{i}\:\mathrm{have}\:\mathrm{seen}\:\mathrm{it}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$