Question Number 222001 by fantastic last updated on 14/Jun/25 $$\left(\frac{\mathrm{4}^{{m}+\frac{\mathrm{1}}{\mathrm{4}}} ×\sqrt{\mathrm{2}.\mathrm{2}^{{m}} }}{\mathrm{2}.\sqrt{\mathrm{2}^{−{m}} }}\right)^{\frac{\mathrm{1}}{{m}}} =?? \\ $$ Commented by fantastic last updated on 16/Jun/25 $${Oooo} \\…
Question Number 222003 by fantastic last updated on 14/Jun/25 $${If}\:{a}+{b}+{c}=\mathrm{0}\:{then}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{{x}^{{b}} +{x}^{−{c}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{c}} +{x}^{−{a}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{a}} +{x}^{−{b}} +\mathrm{1}}=\mathrm{1} \\ $$ Answered by som(math1967) last updated…
Question Number 221991 by hardmath last updated on 14/Jun/25 $$\mathrm{Simplify}:\:\:\:\mathrm{2}^{\mathrm{2}} \:\centerdot\:\mathrm{2}^{\mathrm{2}^{\frac{\mathrm{70}\:−\:\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:\:\:=\:\:\:?} \\ $$ Commented by hardmath last updated on 14/Jun/25 $$\mathrm{yes} \\ $$…
Question Number 221944 by hardmath last updated on 13/Jun/25 Commented by hardmath last updated on 13/Jun/25 $$\mathrm{If}: \\ $$$$\bigtriangleup\mathrm{ABC}\:-\:\mathrm{Equilateral}\:\mathrm{Triangle} \\ $$$$\mathrm{MK}\:\parallel\:\mathrm{AB} \\ $$$$\mathrm{MN}\:\parallel\:\mathrm{AC} \\ $$$$\mathrm{ML}\:\bot\:\mathrm{AB}…
Question Number 221943 by hardmath last updated on 13/Jun/25 Answered by MrGaster last updated on 13/Jun/25 $$\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}{i}\left({k}−{i}+\frac{\mathrm{2}}{\mathrm{3}}\right)=\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}\left({ki}−{i}^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{3}}{i}\right)={k}\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}{i}−\underset{{i}=\mathrm{1}} {\overset{{k}}…
Question Number 221848 by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Terms of…
Question Number 221829 by fantastic last updated on 11/Jun/25 $$\sqrt{\mathrm{70}.\mathrm{71}.\mathrm{72}.\mathrm{73}+\mathrm{1}} \\ $$ Answered by aleks041103 last updated on 11/Jun/25 $$\mathrm{70}.\mathrm{71}.\mathrm{72}.\mathrm{73}+\mathrm{1}= \\ $$$$=\mathrm{70}.\mathrm{73}.\left(\mathrm{70}+\mathrm{1}\right)\left(\mathrm{73}−\mathrm{1}\right)+\mathrm{1}= \\ $$$$=\mathrm{70}.\mathrm{73}.\left(\mathrm{70}.\mathrm{73}+\mathrm{73}−\mathrm{70}−\mathrm{1}\right)+\mathrm{1}= \\…
Question Number 221863 by fantastic last updated on 11/Jun/25 $${If}\:{a}\:{and}\:{b}\:{are}\:{whole}\:{numbers}\:{such}\:{a}^{{b}} =\mathrm{121} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\left({a}−\mathrm{1}\right)^{{b}+\mathrm{1}} \\ $$ Commented by Tawa11 last updated on 11/Jun/25 $$\mathrm{11}^{\mathrm{2}} \:\:=\:\:\mathrm{121} \\…
Question Number 221856 by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Commented by…
Question Number 221791 by hardmath last updated on 10/Jun/25 Commented by hardmath last updated on 10/Jun/25 $$\mathrm{ABC}\:-\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{MK}\:\parallel\:\mathrm{AB} \\ $$$$\mathrm{MN}\:\parallel\:\mathrm{AC} \\ $$$$\mathrm{ML}\:\bot\:\mathrm{AB} \\ $$$$\mathrm{AC}\:=\:\mathrm{a}…