Menu Close

Question-69296




Question Number 69296 by ozodbek last updated on 22/Sep/19
Commented by Prithwish sen last updated on 22/Sep/19
can you post the answer please?
$$\mathrm{can}\:\mathrm{you}\:\mathrm{post}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{please}? \\ $$
Commented by MJS last updated on 22/Sep/19
approximation gives 8
$$\mathrm{approximation}\:\mathrm{gives}\:\mathrm{8} \\ $$
Commented by Prithwish sen last updated on 22/Sep/19
8=3!+2!=(√((3!+2!)^2  )) = (√(2!(2!+2.3!+3.3!)))  =(√(2!{2!+2.3!+3!(4−1)})) = (√(2!{2!+3!+4!)))  =(√(2!{2!+(√((3!+4!)^2 ))))=(√(2!^2 +2!(√(3!(3!+2.4!+4.4!)))))  =(√(2!^2 +2!(√(3!{3!+2.4!+4!(5−1)}))))   =(√(2!^2 +2!(√(3!{3!+(4!+5!)))))   =(√(2!^2 +2!(√(3!^2 +3!(√((4!+5!)^2 ))))))  ......  =(√(2!^2 +2!(√(3!^2 +3!(√(4!^2 +4!(√(.......))))))))  Thanks Sir MJS your approximation help me  a lot. I appreciate your cooperation. Again  thanks a lot.
$$\mathrm{8}=\mathrm{3}!+\mathrm{2}!=\sqrt{\left(\mathrm{3}!+\mathrm{2}!\right)^{\mathrm{2}} \:}\:=\:\sqrt{\mathrm{2}!\left(\mathrm{2}!+\mathrm{2}.\mathrm{3}!+\mathrm{3}.\mathrm{3}!\right)} \\ $$$$=\sqrt{\mathrm{2}!\left\{\mathrm{2}!+\mathrm{2}.\mathrm{3}!+\mathrm{3}!\left(\mathrm{4}−\mathrm{1}\right)\right\}}\:=\:\sqrt{\mathrm{2}!\left\{\mathrm{2}!+\mathrm{3}!+\mathrm{4}!\right)} \\ $$$$=\sqrt{\mathrm{2}!\left\{\mathrm{2}!+\sqrt{\left(\mathrm{3}!+\mathrm{4}!\right)^{\mathrm{2}} }\right.}=\sqrt{\mathrm{2}!^{\mathrm{2}} +\mathrm{2}!\sqrt{\mathrm{3}!\left(\mathrm{3}!+\mathrm{2}.\mathrm{4}!+\mathrm{4}.\mathrm{4}!\right)}} \\ $$$$=\sqrt{\mathrm{2}!^{\mathrm{2}} +\mathrm{2}!\sqrt{\mathrm{3}!\left\{\mathrm{3}!+\mathrm{2}.\mathrm{4}!+\mathrm{4}!\left(\mathrm{5}−\mathrm{1}\right)\right\}}}\: \\ $$$$=\sqrt{\mathrm{2}!^{\mathrm{2}} +\mathrm{2}!\sqrt{\mathrm{3}!\left\{\mathrm{3}!+\left(\mathrm{4}!+\mathrm{5}!\right)\right.}}\: \\ $$$$=\sqrt{\mathrm{2}!^{\mathrm{2}} +\mathrm{2}!\sqrt{\mathrm{3}!^{\mathrm{2}} +\mathrm{3}!\sqrt{\left(\mathrm{4}!+\mathrm{5}!\right)^{\mathrm{2}} }}}\:\:…… \\ $$$$=\sqrt{\mathrm{2}!^{\mathrm{2}} +\mathrm{2}!\sqrt{\mathrm{3}!^{\mathrm{2}} +\mathrm{3}!\sqrt{\mathrm{4}!^{\mathrm{2}} +\mathrm{4}!\sqrt{…….}}}} \\ $$$$\boldsymbol{\mathrm{Thanks}}\:\boldsymbol{\mathrm{Sir}}\:\boldsymbol{\mathrm{MJS}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{approximation}}\:\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{me}} \\ $$$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{lot}}.\:\boldsymbol{\mathrm{I}}\:\boldsymbol{\mathrm{appreciate}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{cooperation}}.\:\boldsymbol{\mathrm{Again}} \\ $$$$\boldsymbol{\mathrm{thanks}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{lot}}. \\ $$
Commented by MJS last updated on 22/Sep/19
great! And as always, you′re welcome
$$\mathrm{great}!\:\mathrm{And}\:\mathrm{as}\:\mathrm{always},\:\mathrm{you}'\mathrm{re}\:\mathrm{welcome} \\ $$
Commented by ozodbek last updated on 23/Sep/19
thank you
$$\mathrm{thank}\:\mathrm{you} \\ $$
Commented by Prithwish sen last updated on 23/Sep/19
you are welcome.
$$\mathrm{you}\:\mathrm{are}\:\mathrm{welcome}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *