Question Number 160564 by Avijit007 last updated on 02/Dec/21 $${if}\:{the}\:{roots}\:{of}\:{th}\mathrm{e}\:{equation}\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0} \\ $$$${are}\:{in}\:{the}\:{ratio}\:\mathrm{3}:\mathrm{4},{then}\:{show}\:{that}\: \\ $$$$\mathrm{12b}^{\mathrm{2}} =\mathrm{49ac}. \\ $$ Commented by otchereabdullai@gmail.com last updated on 02/Dec/21…
Question Number 160560 by HongKing last updated on 01/Dec/21 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on…
Question Number 95014 by I want to learn more last updated on 22/May/20 $$\boldsymbol{\mathrm{If}}\:\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \:\:\:=\:\:\:\mathrm{6},\:\:\:\:\:\:\:\boldsymbol{\mathrm{and}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\mathrm{0}} \:\:=\:\:\:\mathrm{7} \\ $$$$\boldsymbol{\mathrm{Find}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \\ $$ Commented by prakash jain…
Question Number 160550 by HongKing last updated on 01/Dec/21 $$\mathrm{if}\:\:\:\mathrm{x};\mathrm{y}\in\left(\mathrm{0};\frac{\pi}{\mathrm{2}}\right)\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{sin}\boldsymbol{\mathrm{x}}\:+\:\mathrm{sin}\boldsymbol{\mathrm{y}}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\boldsymbol{\mathrm{x}}\:+\:\mathrm{cos}\boldsymbol{\mathrm{y}}}}\:\leqslant\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$ Answered by mr W last updated on 02/Dec/21 $${LHS} \\ $$$$\leqslant\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{sin}\:{x}\:\mathrm{sin}\:{y}}}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{cos}\:{x}\:\mathrm{cos}\:{y}}}}…
Question Number 160522 by mnjuly1970 last updated on 01/Dec/21 Answered by mr W last updated on 03/Dec/21 Commented by mr W last updated on 03/Dec/21…
Question Number 29433 by Victor31926 last updated on 08/Feb/18 $$\mathrm{4}\left(\mathrm{2x}^{\mathrm{2}} \right)=\mathrm{8}^{\mathrm{x}} \\ $$ Answered by mrW2 last updated on 08/Feb/18 $$\Rightarrow\mathrm{8}{x}^{\mathrm{2}} =\mathrm{8}^{{x}} \\ $$$$\Rightarrow\left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)^{\mathrm{2}} =\mathrm{8}^{{x}}…
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Question Number 94960 by bshahid010@gmail.com last updated on 22/May/20 Answered by Kunal12588 last updated on 22/May/20 $$\mathrm{2}+\left({n}−\mathrm{1}\right)\left(\mathrm{3}\right)=\mathrm{2}+\left({n}_{\mathrm{1}} −\mathrm{1}\right)\left(\mathrm{5}\right) \\ $$$$\Rightarrow\mathrm{3}{n}−\mathrm{1}=\mathrm{5}{n}_{\mathrm{1}} −\mathrm{3} \\ $$$$\Rightarrow\mathrm{5}{n}_{\mathrm{1}} −\mathrm{3}{n}=\mathrm{2} \\…
Question Number 29424 by Tinkutara last updated on 08/Feb/18 Commented by prof Abdo imad last updated on 09/Feb/18 $$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{2}^{{n}} \:{n}!}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)}=\sum_{{n}=\mathrm{1}} ^{\infty} \:{u}_{{n}} \\…