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Question Number 107999 by Don08q last updated on 13/Aug/20 Commented by udaythool last updated on 13/Aug/20 $$\Rightarrow\mathrm{4}{x}^{\mathrm{2}} +\mathrm{3}{xy}−{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow\left({x}+{y}\right)\left(\mathrm{4}{x}−{y}\right)=\mathrm{0} \\ $$$$\Rightarrow\mathrm{4}{x}={y};\:\:\:\left(\because\:{x}+{y}\neq\mathrm{0}\right) \\ $$$$\Rightarrow\mathrm{4}{x}^{\mathrm{2}}…
Question Number 173529 by Shrinava last updated on 13/Jul/22 $$\mathrm{Find}\:\mathrm{without}\:\mathrm{softs}:\:\:\:\Omega\:=\:\int_{\frac{\boldsymbol{\pi}}{\mathrm{5}}} ^{\:\frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{10}}} \:\frac{\mathrm{x}}{\mathrm{sin2x}}\:\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 13/Jul/22 $${I}=\int_{\frac{\pi}{\mathrm{5}}} ^{\frac{\mathrm{3}\pi}{\mathrm{10}}} \frac{{x}}{\mathrm{sin2}{x}}{dx}\:,\:{x}=\frac{\pi}{\mathrm{2}}−{u}\:\Rightarrow{I}=\int_{\frac{\pi}{\mathrm{5}}}…
Question Number 173535 by mnjuly1970 last updated on 13/Jul/22 Answered by mr W last updated on 13/Jul/22 $${in}\:{expansion}\:{of}\:\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} +{x}_{\mathrm{3}} +…+{x}_{{n}} \right)^{{m}} \\ $$$${the}\:{general}\:{term}\:{is}\:{x}_{\mathrm{1}} ^{{k}_{\mathrm{1}}…
Question Number 173531 by mnjuly1970 last updated on 13/Jul/22 $$ \\ $$$$\:\:\:\:{Q}: \\ $$$$\:\:{what}\:{is}\:{the}\:{greatest}\:{coefficient} \\ $$$$\:\:{of}\:{the}\:{following}\:\:{expansion}. \\ $$$$\:\:\:\:\:\:\:\mathrm{P}:=\:\left(\:{a}+\:{b}\:+{c}\:+{d}\:\right)^{\:\mathrm{10}} \\ $$$$\:\:\:\:\:\:\:−−−−−−− \\ $$ Answered by mr…
Question Number 107976 by anonymous last updated on 13/Aug/20 $${Rewrite}\:\mathrm{cos6}{x}\mathrm{cos}\:\mathrm{4}{x}\:{as}\:{a}\:{sum}\:{or} \\ $$$${difference} \\ $$ Answered by mathmax by abdo last updated on 13/Aug/20 $$\mathrm{cos}\left(\mathrm{4x}\right)\mathrm{cos}\left(\mathrm{6x}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\left\{\mathrm{cos}\left(\mathrm{10x}\right)\:+\mathrm{cos}\left(\mathrm{2x}\right)\right\} \\…