Question Number 76307 by Master last updated on 26/Dec/19 Answered by mr W last updated on 26/Dec/19 $${x}\neq\mathrm{1} \\ $$$$\mathrm{125}\left(\mathrm{1}+{x}^{\mathrm{5}} \right)=\mathrm{11}\left(\mathrm{1}+{x}\right)^{\mathrm{5}} \\ $$$$\mathrm{125}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…
Question Number 10755 by Joel576 last updated on 24/Feb/17 $${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{xy}\:+\:\mathrm{2}\left({x}\:−\:{y}\right)\:=\:\mathrm{9} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{solution}\:\mathrm{that}\:\mathrm{fulfilled}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{above}\:? \\ $$$${x},\:{y}\:\in\:\mathbb{N} \\ $$ Answered by mrW1 last updated on 24/Feb/17…
Question Number 76290 by benjo last updated on 26/Dec/19 $$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{x}^{\mathrm{y}} \:+\mathrm{y}^{\mathrm{x}} \:\geqslant\mathrm{1}\:,\:\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$$$\mathrm{x},\mathrm{y}\:>\:\mathrm{0} \\ $$ Commented by MJS last updated on 26/Dec/19 $$\mathrm{we}\:\mathrm{can}\:\mathrm{exchange}\:{x}\:\mathrm{and}\:{y}\:\Rightarrow\:\mathrm{let}\:{x}\leqslant{y} \\…
Question Number 141822 by mathsuji last updated on 23/May/21 Commented by MJS_new last updated on 23/May/21 $$\mathrm{where}\:\mathrm{you}\:\mathrm{found}\:\mathrm{this}? \\ $$$$\mathrm{did}\:\mathrm{your}\:\mathrm{teacher}\:\mathrm{gave}\:\mathrm{it}\:\mathrm{to}\:\mathrm{you}?\:\mathrm{which}\:\mathrm{chapter} \\ $$$$\mathrm{of}\:\mathrm{solving}\:\mathrm{equations}\:\mathrm{are}\:\mathrm{you}\:\mathrm{studying}? \\ $$$$\mathrm{have}\:\mathrm{you}\:\mathrm{got}\:\mathrm{any}\:\mathrm{idea}? \\ $$$$\bullet\:\mathrm{yes}:\:\mathrm{then}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{us}…
Question Number 141812 by mathsuji last updated on 23/May/21 Commented by mr W last updated on 23/May/21 $${check}\:{your}\:{question}\:{and}\:{diagram}! \\ $$$$\angle{BEC}=\alpha\:? \\ $$$${but}\:{according}\:{to}\:{diagram} \\ $$$$\angle{BEC}=\mathrm{180}° \\…
Question Number 76277 by TawaTawa last updated on 25/Dec/19 Answered by MJS last updated on 25/Dec/19 $$\left(\mathrm{1}\right)\:\Rightarrow\:{y}=\mathrm{4}−\mathrm{2}{x} \\ $$$$\Rightarrow \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{4}\left(\mathrm{4}−{x}\right)^{\mathrm{4}−{x}} ={x}\left(\mathrm{4}−\mathrm{2}{x}\right)^{\mathrm{2}} \mathrm{3}^{\mathrm{4}−{x}} \\ $$$$\mathrm{let}\:{t}=\mathrm{4}−{x}\:\Leftrightarrow\:{x}=\mathrm{4}−{t}…
Question Number 141814 by gsk2684 last updated on 12/Jul/21 $${please}\:{help}\:{me}\:{finding}\:{the}\:{roots}\:{of}\:\: \\ $$$${x}^{\mathrm{5}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{20}{x}^{\mathrm{3}} +\mathrm{60}{x}^{\mathrm{2}} +\mathrm{120}{x}+\mathrm{120}=\mathrm{0}? \\ $$ Commented by MJS_new last updated on 23/May/21…
Question Number 10734 by ABD last updated on 23/Feb/17 $${f}\left({x}−\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{6}\:\Rightarrow{f}\left({x}\right)=? \\ $$ Answered by bar Jesús last updated on 23/Feb/17 $${y}\mathrm{1}={f}\left({x}−\mathrm{1}\right)=\mathrm{2}\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{6} \\ $$$${y}\mathrm{2}={f}\left({x}+\mathrm{1}\right)=\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 10721 by niraj last updated on 23/Feb/17 $${Q}.\mathrm{1}\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −{i}\left(\mathrm{2}{x}+{y}\right)=\mathrm{2}{i} \\ $$$${Q}.\mathrm{2}\:\:\:\left(\mathrm{2}+\mathrm{3}{i}\right){x}^{\mathrm{2}} −\left(\mathrm{3}−{x}\right){y}=\mathrm{2}{x}−\mathrm{3}{y} \\ $$ Answered by sandy_suhendra last updated on 23/Feb/17 $$\mathrm{Q}.\mathrm{1}…
Question Number 141794 by mathdanisur last updated on 23/May/21 Commented by JDamian last updated on 23/May/21 $${repeated}\:{question}\:\mathrm{141730} \\ $$ Commented by mathdanisur last updated on…