Question Number 60054 by bhanukumarb2@gmail.com last updated on 17/May/19 Commented by bhanukumarb2@gmail.com last updated on 17/May/19 $${is}\:{titu}\:{lemma}\:{applicable}\:{here}??{plz}\:{see} \\ $$$${previous}\:{doubts} \\ $$ Answered by tanmay last…
Question Number 191028 by Mingma last updated on 16/Apr/23 Answered by Frix last updated on 16/Apr/23 $$\mathrm{Not}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{but}\:\mathrm{an}\:\mathrm{idea}\:\mathrm{for}\:\mathrm{a}\:\mathrm{proof}: \\ $$$$\left({n}−\mathrm{1}\right){n}\left({n}+\mathrm{1}\right)×{N}={k}^{\mathrm{3}} ;\:{k}\in\mathbb{N} \\ $$$$\mathrm{We}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{1}.\:\mathrm{gcd}\:\left({n}−\mathrm{1},\:{n}\right)\:=\mathrm{1} \\…
Question Number 191025 by Rupesh123 last updated on 16/Apr/23 Commented by Rasheed.Sindhi last updated on 17/Apr/23 $${n}=\mathrm{8} \\ $$$$\overset{×} {\mathrm{1}},\overset{×} {\mathrm{2}},\mathrm{3},\overset{×} {\mathrm{4}},\mathrm{5},\overset{×} {\mathrm{6}},\mathrm{7} \\ $$$$\:\:\:\:\left(\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{6}\:{are}\:{not}\:{relatively}\:{prime}\right)…
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Question Number 125314 by peter frank last updated on 10/Dec/20 $$\mathrm{make}\:\mathrm{x}\:\mathrm{the}\:\mathrm{subject} \\ $$$$\mathrm{y}=\mathrm{x}! \\ $$ Commented by john_santu last updated on 10/Dec/20 $${may}\:{be}\:{make}\:{x}\:{as}\:{predicat}\: \\ $$…
Question Number 59763 by ANTARES VY last updated on 14/May/19 $$\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{2}}−\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}} \\ $$$$\boldsymbol{\mathrm{simplify}}. \\ $$ Answered by Kunal12588 last updated on 14/May/19 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}=\sqrt{\frac{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{2}}} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}=\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{2}}}…
Question Number 59562 by shaifalzhob last updated on 11/May/19 $$\left.\mathrm{Derive}\:\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{motion}\:\mathrm{1}\right)\mathrm{Vu}+\mathrm{at} \\ $$ Answered by Forkum Michael Choungong last updated on 11/May/19 $${remeber}\:\:{a}=\frac{\bigtriangleup{v}}{{t}} \\ $$$$\Rightarrow{a}\:=\:\frac{{v}−{u}}{{t}} \\…
Question Number 190618 by mustafazaheen last updated on 07/Apr/23 $$\mathrm{f}\left(\mathrm{x}−\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}\:\:,\mathrm{f}\left(\mathrm{5}\right)=−\mathrm{1} \\ $$$$\mathrm{f}\left(−\mathrm{1}\right)=? \\ $$ Answered by aba last updated on 07/Apr/23 $$\mathrm{f}\left(\mathrm{5}−\mathrm{f}\left(\mathrm{5}\right)\right)=\mathrm{5}\Rightarrow\:\mathrm{f}\left(\mathrm{4}\right)=\mathrm{5} \\ $$$$\mathrm{f}\left(\mathrm{4}−\mathrm{f}\left(\mathrm{4}\right)\right)=\mathrm{4}\Rightarrow\mathrm{f}\left(−\mathrm{1}\right)=\mathrm{4} \\…
Question Number 190395 by mr W last updated on 02/Apr/23 $${which}\:{is}\:{larger}, \\ $$$$\mathrm{2}^{\mathrm{234}} \:{or}\:\mathrm{5}^{\mathrm{100}} \:? \\ $$ Answered by aba last updated on 02/Apr/23 $$\mathrm{2}^{\mathrm{234}}…
Question Number 59316 by mr W last updated on 07/May/19 Answered by MJS last updated on 07/May/19 $${a}+{b}+{c}=\mathrm{25}\:\wedge\:{a},\:{b},\:{c}\:\in\mathbb{N}^{\bigstar} \:\Rightarrow\:\mathrm{1}\leqslant{a},\:{b},\:{c}\leqslant\mathrm{23} \\ $$$$\mathbb{S}=\left\{{n}\in\mathbb{N}^{\bigstar} \mid\mathrm{1}\leqslant{n}\leqslant\mathrm{23}\:\wedge\:\mathrm{mod}\left(\mathrm{360},\:{n}\right)=\mathrm{0}\right\}= \\ $$$$=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{8},\:\mathrm{9},\:\mathrm{10},\:\mathrm{12},\:\mathrm{15},\:\mathrm{18},\:\mathrm{20}\right\} \\…