Question Number 152753 by mathdanisur last updated on 01/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{triplets}\:\left(\mathrm{a};\mathrm{b};\mathrm{c}\right)\:\mathrm{of}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{which}\:\mathrm{satisfy}: \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by Rasheed.Sindhi last updated on 01/Sep/21 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{triplets}\:\left(\mathrm{a};\mathrm{b};\mathrm{c}\right)\:\mathrm{of}\:\mathrm{positive} \\…
Question Number 152752 by EDWIN88 last updated on 01/Sep/21 $$\:{Given}\:\sqrt[{\mathrm{3}}]{\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}+\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{2}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{2}}}\:=\mathrm{2} \\ $$$${then}\:\sqrt{\mathrm{198}{x}^{\mathrm{4}} −\mathrm{868}{x}^{\mathrm{3}} −\mathrm{229}{x}^{\mathrm{2}} +\mathrm{200}{x}}\:=? \\ $$ Commented by liberty last updated on 01/Sep/21 x = 4.5897576…
Question Number 21653 by Joel577 last updated on 30/Sep/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{solutions}\:\left({x},{y}\right)\:\mathrm{that}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{7}{x}^{\mathrm{2}} \:−\:\mathrm{13}{xy}\:+\:\mathrm{7}{y}^{\mathrm{2}} }\:=\:\mid{x}\:−\:{y}\mid\:+\:\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21654 by Joel577 last updated on 30/Sep/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:{Q}\:\mathrm{that}\:\mathrm{satisfy}: \\ $$$$\mid{xy}\left({x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \right)\:+\:{yz}\left({y}^{\mathrm{2}} \:−\:{z}^{\mathrm{2}} \right)\:+\:{zx}\left({z}^{\mathrm{2}} \:−\:{x}^{\mathrm{2}} \right)\mid\:\leqslant\:{Q}\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$ Terms of…
Question Number 21650 by Glorious Man last updated on 30/Sep/17 $${The}\:{three}\:{distinct}\:{successive}\:{terms}\:{of}\:{an}\:{A}.{P}\:{are} \\ $$$${the}\:{first},{second}\:{and}\:{fourth}\:{terms}\:{of}\:{a}\:{G}.{P}.\:{If}\:{the}\: \\ $$$${sum}\:{to}\:{infinity}\:{of}\:{a}\:{G}.{P}\:{is}\:\mathrm{3}+\sqrt{\mathrm{5}}\:,\:{find}\: \\ $$$${the}\:{first}\:{term}. \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 21643 by Joel577 last updated on 30/Sep/17 $$\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{1}^{\mathrm{4}} }\:+\:\frac{\mathrm{2}}{\mathrm{1}\:+\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{2}^{\mathrm{4}} }\:+\:\frac{\mathrm{3}}{\mathrm{1}\:+\:\mathrm{3}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{4}} }\:+\:…\:+\:\frac{\mathrm{2012}}{\mathrm{1}\:+\:\mathrm{2012}^{\mathrm{2}} \:+\:\mathrm{2012}^{\mathrm{4}} } \\ $$ Commented by Joel577 last updated…
Question Number 152697 by mathdanisur last updated on 31/Aug/21 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\left(\mathrm{r}_{\boldsymbol{\mathrm{a}}} +\mathrm{r}_{\boldsymbol{\mathrm{b}}} \right)\left(\mathrm{r}_{\boldsymbol{\mathrm{a}}} +\mathrm{r}_{\boldsymbol{\mathrm{c}}} \right)}{\mathrm{h}_{\boldsymbol{\mathrm{b}}} +\mathrm{h}_{\boldsymbol{\mathrm{c}}} }\:\geqslant\:\frac{\mathrm{9r}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy…
Question Number 21622 by Joel577 last updated on 29/Sep/17 $$\mathrm{If}\:\mathrm{sec}\:{x}\:+\:\mathrm{tan}\:{x}\:=\:\mathrm{2012} \\ $$$$\mathrm{then}\:\mathrm{2011}\left(\mathrm{cosec}\:{x}\:+\:\mathrm{cot}\:{x}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left({A}\right)\:\mathrm{2011} \\ $$$$\left({B}\right)\:\mathrm{2012} \\ $$$$\left({C}\right)\:\mathrm{2013} \\ $$$$\left({D}\right)\:\frac{\mathrm{2011}}{\mathrm{2013}} \\ $$$$\left({E}\right)\:\frac{\mathrm{2013}}{\mathrm{2012}} \\ $$ Answered…
Question Number 152678 by mathdanisur last updated on 31/Aug/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\mathrm{a}^{\mathrm{3}} -\mathrm{6a}^{\mathrm{2}} +\mathrm{15a}-\mathrm{17}=\mathrm{0}\:\:\:\mathrm{and} \\ $$$$\mathrm{a}^{\mathrm{3}} -\mathrm{6a}^{\mathrm{2}} +\mathrm{15a}-\mathrm{11}=\mathrm{0} \\ $$ Answered by mr W last…
Question Number 87130 by jagoll last updated on 03/Apr/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{at}\:\theta\:=\frac{\pi}{\mathrm{4}}\:? \\ $$ Commented by mr W last updated on 03/Apr/20 $${y}={r}\:\mathrm{sin}\:\theta=\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{sin}\:\theta \\ $$$${x}={r}\:\mathrm{cos}\:\theta=\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{cos}\:\theta…