Question Number 83373 by Power last updated on 01/Mar/20 Commented by jagoll last updated on 02/Mar/20 $$\left(\mathrm{ax}+\mathrm{by}\right)\left(\mathrm{x}+\mathrm{y}\right)\:=\:\mathrm{5}\left(\mathrm{x}+\mathrm{y}\right) \\ $$$$\mathrm{ax}^{\mathrm{2}} +\mathrm{by}^{\mathrm{2}} +\mathrm{axy}+\mathrm{bxy}=\mathrm{5}\left(\mathrm{x}+\mathrm{y}\right) \\ $$$$\mathrm{10}\:+\:\mathrm{xy}\:\left(\mathrm{a}+\mathrm{b}\right)=\:\mathrm{5}\left(\mathrm{x}+\mathrm{y}\right)\:\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{ax}^{\mathrm{2}}…
Question Number 83372 by Power last updated on 01/Mar/20 Commented by mr W last updated on 01/Mar/20 $${goh}\left({x}\right)={x}−\mathrm{2} \\ $$$$\frac{\mathrm{5}{h}\left({x}\right)}{{h}\left({x}\right)+\mathrm{1}}={x}−\mathrm{2} \\ $$$$\Rightarrow{h}\left({x}\right)=\frac{{x}−\mathrm{2}}{\mathrm{7}−{x}} \\ $$$${hof}\left({x}\right)=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)−\mathrm{2}}{\mathrm{7}−\left(\mathrm{2}{x}−\mathrm{1}\right)}=\frac{\mathrm{2}{x}−\mathrm{3}}{\mathrm{8}−\mathrm{2}{x}} \\…
Question Number 83370 by Power last updated on 01/Mar/20 Commented by Power last updated on 01/Mar/20 $$\mathrm{solve}\:\mathrm{pls} \\ $$ Commented by mr W last updated…
Question Number 148890 by mathdanisur last updated on 01/Aug/21 $${if}\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\sqrt{\mathrm{3}} \\ $$$${find}\:\:\:{x}^{\mathrm{18}} \:+\:{x}^{\mathrm{12}} \:+\:{x}^{\mathrm{6}} \:+\:\mathrm{1}\:=\:? \\ $$ Answered by nimnim last updated on 01/Aug/21 $$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\sqrt{\mathrm{3}}\Rightarrow\mathrm{x}^{\mathrm{2}}…
Question Number 148887 by mathdanisur last updated on 01/Aug/21 $$\Omega=\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\sqrt{{x}}\:{ln}\:{x}}{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:{dx}\:=\:? \\ $$ Answered by Kamel last updated on 01/Aug/21 $$\Omega=\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\sqrt{{x}}\:{ln}\:{x}}{{x}^{\mathrm{2}}…
Question Number 83341 by mr W last updated on 01/Mar/20 $${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${of}\:{the}\:{expression}\:\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{a}}_{\boldsymbol{{i}}} \boldsymbol{{x}}_{\boldsymbol{{i}}} \:{with} \\ $$$$\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\left(\boldsymbol{{x}}_{\boldsymbol{{i}}} −\boldsymbol{{b}}_{\boldsymbol{{i}}} \right)^{\mathrm{2}} =\boldsymbol{{c}}^{\mathrm{2}} ,\:{where}\:\boldsymbol{{a}}_{\boldsymbol{{i}}}…
Question Number 148861 by mathdanisur last updated on 31/Jul/21 Answered by dumitrel last updated on 01/Aug/21 $$\left(\mathrm{2}{x}\right)^{\mathrm{4}} +\mathrm{324}=\left(\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{18}\right)\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{18}\right) \\ $$$${f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{18}\Rightarrow{f}\left({x}+\mathrm{3}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{18} \\…
Question Number 17775 by gourav~ last updated on 10/Jul/17 $$\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\frac{\mathrm{sin}\:\mathrm{2}\pi{m}}{\mathrm{11}}\:−\:{i}\frac{\mathrm{cos}\:\mathrm{2}\pi{m}}{\mathrm{11}}\right)\:=????? \\ $$$${Solve}..{it} \\ $$$$ \\ $$ Answered by alex041103 last updated on 10/Jul/17…
Question Number 148838 by liberty last updated on 31/Jul/21 $$\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}×\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{6}×\mathrm{7}×\mathrm{8}}+…+\frac{\mathrm{1}}{\mathrm{12}×\mathrm{13}×\mathrm{14}}=? \\ $$ Commented by JDamian last updated on 31/Jul/21 $${Can}\:{you}\:{confirm}\:{there}\:{is}\:{a}\:{missing}\:\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}? \\ $$ Commented by liberty…
Question Number 17759 by chux last updated on 10/Jul/17 $$\mathrm{2}^{\mathrm{4}\left(\mathrm{y}^{\mathrm{2}} −\mathrm{2}\right)} =\mathrm{y}^{\left(\mathrm{y}^{\mathrm{2}} −\mathrm{8}\right)} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{find}\:\mathrm{y}…\:\mathrm{pls}! \\ $$ Answered by mrW1 last…