Question Number 212231 by Davidtim last updated on 07/Oct/24
$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}{cos}\mathrm{8}{x}}}}}=? \\ $$
Commented by Davidtim last updated on 07/Oct/24
$${please}\:{help}\:{me} \\ $$
Commented by mr W last updated on 08/Oct/24
$${then}\:{at}\:{first}\:{you}\:{should}\:{help}\:{other} \\ $$$${people}\:{to}\:{understand}\:{what}\:{you}\:{want} \\ $$$${other}\:{people}\:{do}. \\ $$
Commented by Ghisom last updated on 08/Oct/24
$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{anybody}\:\mathrm{can}\:\mathrm{help}\:\mathrm{here} \\ $$$$\mathrm{what}\:\mathrm{are}\:\mathrm{we}\:\mathrm{supposed}\:\mathrm{to}\:\mathrm{do}? \\ $$
Commented by Davidtim last updated on 08/Oct/24
$${why}?!\:{we}\:{all}\:{should}\:{help}\:{each}\:{other} \\ $$$${this}\:{APP}\:{relates}\:{to}\:{helping}\:{and}\:{educating}. \\ $$
Commented by Davidtim last updated on 08/Oct/24
$$? \\ $$
Commented by Davidtim last updated on 08/Oct/24
$${If}\:{I}\:{cant}\:{solve}\:{the}\:{problem}\:{then}\:{need} \\ $$$${your}\:{help}. \\ $$
Commented by mr W last updated on 08/Oct/24
$${it}'{s}\:{not}\:{that}\:{they}\:{don}'{t}\:{help}\:{you},\:{but} \\ $$$${they}\:{don}'{t}\:{know}\:{what}\:{you}\:{expect}. \\ $$$${if}\:{you}\:{want}\:{to}\:{simply}\:{the}\:{expression}, \\ $$$${i}\:{think}\:{you}\:{can}\:{not}\:{simply}\:{it}\:{more}. \\ $$
Commented by Davidtim last updated on 08/Oct/24
$${Ok}\:{sir}\:{I}\:{have}\:{uploaded}\:{the}\:{problem} \\ $$$${and}\:{I}\:{have}\:{expected}\:{of}\:{solotion}\:{the}\:{problem}. \\ $$$${I}\:{mention}\:{again}\:{here}\:{please}\:{solve}\:{this}. \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}{cos}\mathrm{8}{x}}}}}=? \\ $$
Commented by mr W last updated on 08/Oct/24
$${i}\:{have}\:{told}\:{you}\:{that}\:{this}\:{expression} \\ $$$${can}\:{not}\:{be}\:{simplied}\:{further}. \\ $$
Commented by Davidtim last updated on 08/Oct/24
$${ok}\:{sir}\:{thanks}\:{lots}\:{of}. \\ $$
Commented by TonyCWX08 last updated on 08/Oct/24
$${You}\:{guve}\:{us}\:{an}\:{expression}\:{and}\:{expect}\:{us}\:{to}\:{simplify}\:{it}?? \\ $$
Answered by ajfour last updated on 08/Oct/24
$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}{cos}\mathrm{8}{x}}}}}={q} \\ $$$$\left\{\left({q}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{2}} −\mathrm{2}\right\}^{\mathrm{2}} =\mathrm{2}+\sqrt{\mathrm{2cos}\:\mathrm{8}{x}} \\ $$$${let}\:\:\mathrm{cos}\:\mathrm{8}{x}=\mathrm{2cos}\:^{\mathrm{2}} \mathrm{8}\theta \\ $$$$\Rightarrow\:\:\left({q}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{2}} =\mathrm{2}+\mathrm{2cos}\:\mathrm{4}\theta \\ $$$$\Rightarrow\:{q}^{\mathrm{2}} =\mathrm{2}+\mathrm{2cos}\:\mathrm{2}\theta \\ $$$$\:\:\:\:{q}=\mathrm{2cos}\:\theta\: \\ $$$$\:\:\:\:\:\:=\:\mathrm{2cos}\:\left[\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}^{−\mathrm{1}} \sqrt{\frac{\mathrm{cos}\:\mathrm{8}{x}}{\mathrm{2}}}\right] \\ $$
Commented by TonyCWX08 last updated on 08/Oct/24
$${Nah}\:{its}\:{wrong}. \\ $$$${You}\:{compared}\: \\ $$$${cos}\left(\mathrm{8}{x}\right)\:{and}\:\mathrm{2}{cos}^{\mathrm{2}} \left(\mathrm{8}\theta\right),\:{which}\:{is}\:{two}\:{different}\:{thingd}. \\ $$
Commented by ajfour last updated on 08/Oct/24
$${lets}\:{wait}\:{for}\:{other}\:{expert}\:{comments} \\ $$