Question Number 95222 by bobhans last updated on 24/May/20 $$\begin{cases}{{x}^{\mathrm{2}} \:+\:{x}\:\sqrt[{\mathrm{3}\:\:}]{{xy}^{\mathrm{2}} }\:=\:\mathrm{80}\:}\\{{y}^{\mathrm{2}} \:+\:{y}\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{2}} {y}}\:=\:\mathrm{5}\:}\end{cases} \\ $$$${find}\:{x}\:{and}\:{y}\: \\ $$ Answered by john santu last updated on…
Question Number 160744 by cortano last updated on 05/Dec/21 $$\:\:\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{12}\right)^{\mathrm{3}} +\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{18}\right)^{\mathrm{2}} =\:\mathrm{9}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{2}} \\ $$$$\:\mathrm{x}=?\: \\ $$ Commented by blackmamba last updated on…
Question Number 95182 by i jagooll last updated on 23/May/20 Answered by mr W last updated on 23/May/20 $$\frac{\mathrm{1}}{{S}}+\frac{\mathrm{1}}{{S}+\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{5}} \\ $$$${S}^{\mathrm{2}} −\mathrm{6}{S}−\mathrm{20}=\mathrm{0} \\ $$$${S}=\mathrm{3}+\sqrt{\mathrm{29}}\approx\mathrm{8}.\mathrm{4}\:{h} \\…
Question Number 29647 by rahul 19 last updated on 11/Feb/18 Commented by rahul 19 last updated on 11/Feb/18 $$?×?×?+?×?×?×? \\ $$ Terms of Service Privacy…
Question Number 160712 by HongKing last updated on 05/Dec/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\left(\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3n}^{\mathrm{2}} }{\mathrm{4n}^{\mathrm{2}} }\right)^{\mathrm{4}} =\:\frac{\mathrm{2}}{\mathrm{n}}\:\mathrm{y}-\mathrm{1}\:\:;\:\:\left(\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3n}^{\mathrm{2}} }{\mathrm{4n}^{\mathrm{2}} }\right)^{\mathrm{4}} =\:\frac{\mathrm{2}}{\mathrm{n}}\:\mathrm{z}-\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3n}^{\mathrm{2}} }{\mathrm{4n}^{\mathrm{2}} }\right)^{\mathrm{4}}…
Question Number 160711 by HongKing last updated on 05/Dec/21 $$\mathrm{Be}\:\:\boldsymbol{\mathrm{p}}\:\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:,\:\mathrm{arbitrary}. \\ $$$$\mathrm{Solve}\:\mathrm{on}\:\mathrm{positive}\:\mathrm{integers}\:\:\left(\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}};\boldsymbol{\mathrm{z}}\right) \\ $$$$\begin{cases}{\mathrm{xy}\:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{3p}\:+\:\mathrm{4}}\\{\mathrm{x}\:+\:\mathrm{yz}^{\mathrm{2}} \:=\:\mathrm{p}\:+\:\mathrm{4}}\end{cases} \\ $$ Answered by mr W last updated on…
Question Number 160706 by HongKing last updated on 05/Dec/21 Answered by mr W last updated on 05/Dec/21 $${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}\:\left(\frac{{k}}{{n}^{\mathrm{3}} }\right) \\ $$$${T}_{{n}} =\underset{{k}=\mathrm{1}}…
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Question Number 95167 by Rio Michael last updated on 23/May/20 $$\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{in}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{is}\:\frac{\left(\mathrm{2}{x}\:+\:\mathrm{7}\right)}{\mathrm{2}{x}−\mathrm{5}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{is} \\ $$$$\:\frac{\left(\mathrm{2}{x}−\mathrm{5}\right)}{\mathrm{2}{x}\:+\:\mathrm{7}}\:\mathrm{find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{for}\:\mathrm{which}\:\mathrm{all}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{possible}. \\ $$ Commented by john santu last updated on 23/May/20 $$\left(\mathrm{1}\right)\:\mathrm{x}\:\neq\:\frac{\mathrm{5}}{\mathrm{2}}\:\wedge\:\mathrm{x}\:\neq\:−\frac{\mathrm{7}}{\mathrm{2}}\: \\…
Question Number 95164 by mr W last updated on 23/May/20 $${if}\:{a}_{{k}} =\mathrm{tan}\:\left(\theta+\frac{{k}\pi}{{n}}\right), \\ $$$${find}\:\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} }{\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{a}_{{k}} }=? \\ $$ Commented by MJS…