Question Number 217733 by Samuel12 last updated on 19/Mar/25 Answered by vnm last updated on 19/Mar/25 $${x}^{\frac{\mathrm{1}}{\mathrm{ln}\:\left({e}^{{x}} −\mathrm{1}\right)}} ={e}^{\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:\left({e}^{{x}} −\mathrm{1}\right)}} ={e}^{\frac{\mathrm{ln}\:{x}}{\mathrm{ln}\:{x}+\mathrm{ln}\:\frac{{e}^{{x}} −\mathrm{1}}{{x}}}} = \\ $$$${e}^{\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{ln}\:{x}}\mathrm{ln}\:\frac{{e}^{{x}}…
Question Number 217735 by ArshadS last updated on 19/Mar/25 $$\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}=\:\mathrm{abc} \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:=\:\mathrm{49}\: \\ $$$$\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=?\:\:\:.\:\:\:\:\:\:\:\:\:\:\:.\:\:\:\:\:\:\:\: \\ $$ Commented by mr W last updated…
Question Number 217730 by ArshadS last updated on 19/Mar/25 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:;\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }=? \\ $$ Answered by Wuji last updated on 19/Mar/25 $${let}\:{S}_{{n}} ={x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }…
Question Number 217690 by hardmath last updated on 18/Mar/25 Commented by hardmath last updated on 18/Mar/25 $$\bigstar\mathrm{Hard}\bigstar \\ $$ Commented by mr W last updated…
Question Number 217660 by ArshadS last updated on 17/Mar/25 $$\:{f}\left({x}\right)\:+\:{f}\left({y}\right)={f}\left({x}+{y}\right)+{xy}\: \\ $$$${f}\left({x}\right)=? \\ $$ Answered by vnm last updated on 19/Mar/25 $${f}\left({x}\right)+{f}\left(\mathrm{0}\right)={f}\left({x}+\mathrm{0}\right)+{x}\centerdot\mathrm{0}\:\Rightarrow\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${f}\left({x}\right)+{f}\left(−{x}\right)={f}\left({x}−{x}\right)+{x}\left(−{x}\right)=−{x}^{\mathrm{2}} \\…
Question Number 217659 by ArshadS last updated on 17/Mar/25 $${x}+{y}=\mathrm{7}\:\wedge\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} =\mathrm{133};\:{x},{y}=? \\ $$ Answered by Frix last updated on 17/Mar/25 $$\mathrm{2}+\mathrm{5}=\mathrm{7} \\ $$$$\mathrm{8}+\mathrm{125}=\mathrm{133} \\…
Question Number 217643 by Rojarani last updated on 17/Mar/25 $$\:{a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} +{c}^{\frac{\mathrm{1}}{\mathrm{3}}} =\frac{\mathrm{1}}{\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{3}}} −\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} } \\ $$$$\:\:{b}+{c}−{a}=? \\ $$ Answered by mehdee7396 last updated on…
Question Number 217664 by hardmath last updated on 17/Mar/25 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{2x}\:+\:\mathrm{3}} \\ $$$$\mathrm{prove}\:\mathrm{that}:\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2x}\:+\:\mathrm{3}}}\: \\ $$ Answered by SdC355 last updated on 18/Mar/25 $${f}^{\left(\mathrm{1}\right)} \left({x}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}}. \\…
Question Number 217579 by Rasheed.Sindhi last updated on 16/Mar/25 $$\mathrm{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$$$\mathrm{Altered}\:\mathrm{Question}#\:\mathrm{217541} \\ $$ Commented by Ghisom last updated on…
Question Number 217535 by ArshadS last updated on 15/Mar/25 $$\mathrm{A}\:\mathrm{two}-\mathrm{digit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{When} \\ $$$$\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{reversed},\:\mathrm{the}\:\mathrm{new}\:\mathrm{number} \\ $$$$\:\mathrm{is}\:\mathrm{28}\:\mathrm{less}\:\mathrm{than}\:\mathrm{twice}\:\mathrm{the}\:\:\mathrm{original}\:\mathrm{number}. \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number}. \\ $$ Answered by aleks041103 last updated…