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Category: Algebra

Question-181923

Question Number 181923 by manxsol last updated on 02/Dec/22 Answered by SEKRET last updated on 02/Dec/22 $$\:\:\:\boldsymbol{\mathrm{xlog}}\mathrm{2}\left(\boldsymbol{\mathrm{y}}\right)=\mathrm{6}\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{y}}=\mathrm{2}^{\frac{\mathrm{6}}{\boldsymbol{\mathrm{x}}}} \\ $$$$\:\left(\frac{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}\right)\boldsymbol{\mathrm{log}}\mathrm{2}\left(\boldsymbol{\mathrm{y}}\right)=\mathrm{4} \\ $$$$\:\:\frac{\mathrm{6}}{\boldsymbol{\mathrm{x}}}=\:\frac{\mathrm{4}\boldsymbol{\mathrm{x}}−\mathrm{4}\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}\:\:\:\:\:\:\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{6}\boldsymbol{\mathrm{y}}=\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{xy}} \\ $$$$\:\:\boldsymbol{\mathrm{y}}\left(\mathrm{6}+\mathrm{4}\boldsymbol{\mathrm{x}}\right)=\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{\mathrm{x}}\:\:\:\:\:\boldsymbol{\mathrm{y}}=\:\frac{\boldsymbol{\mathrm{x}}\left(\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\right)}{\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)}…

Question-181902

Question Number 181902 by Acem last updated on 01/Dec/22 Answered by Rasheed.Sindhi last updated on 02/Dec/22 $$\left({x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:=\mathrm{185}….\left({i}\right) \\ $$$$\left({x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}}…

Question-181897

Question Number 181897 by Acem last updated on 01/Dec/22 Answered by mr W last updated on 02/Dec/22 $${T}_{{k}} =\frac{{k}^{\mathrm{2}} }{{k}^{\mathrm{2}} −\mathrm{10}{k}+\mathrm{50}}=\frac{{k}^{\mathrm{2}} }{\left({k}−\mathrm{5}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} } \\…

x-4-ax-2-by-2-y-4-bx-2-ay-2-solve-for-x-y-a-b-R-a-b-0-

Question Number 50825 by behi83417@gmail.com last updated on 20/Dec/18 $$\boldsymbol{\mathrm{x}}^{\mathrm{4}} =\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\boldsymbol{\mathrm{by}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{y}}^{\mathrm{4}} =\boldsymbol{\mathrm{bx}}^{\mathrm{2}} +\boldsymbol{\mathrm{ay}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}},\:\boldsymbol{\mathrm{y}}.\:\left[\boldsymbol{\mathrm{a}}\:,\boldsymbol{\mathrm{b}}\in\:\boldsymbol{\mathrm{R}};\:\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\neq\mathrm{0}\right] \\ $$ Answered by mr W last…

Given-that-17-27-4-6-1-3-and-17-27-4-6-1-3-are-the-roots-of-the-equation-x-2-ax-b-0-Find-the-value-of-ab-

Question Number 116358 by bemath last updated on 03/Oct/20 $$\mathrm{Given}\:\mathrm{that}\:\sqrt[{\mathrm{3}\:}]{\mathrm{17}−\frac{\mathrm{27}}{\mathrm{4}}\sqrt{\mathrm{6}}}\:\mathrm{and}\:\sqrt[{\mathrm{3}\:}]{\mathrm{17}+\frac{\mathrm{27}}{\mathrm{4}}\sqrt{\mathrm{6}}} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{ax}+\mathrm{b}\:=\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{ab}. \\ $$ Answered by MJS_new last updated on 03/Oct/20 $$\sqrt[{\mathrm{3}}]{\mathrm{17}\pm\frac{\mathrm{27}\sqrt{\mathrm{6}}}{\mathrm{4}}}=\mathrm{2}\pm\frac{\sqrt{\mathrm{6}}}{\mathrm{2}}…

1-Let-a-b-and-c-real-number-such-that-ab-a-b-1-3-bc-b-c-1-4-and-ac-a-c-1-5-Find-the-value-of-24abc-ab-ac-bc-2-Let-p-and-q-be-two-real-number-that-satisfy-p-

Question Number 116323 by bobhans last updated on 03/Oct/20 $$\left(\mathrm{1}\right)\mathrm{Let}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}\:=\:\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{bc}}{\mathrm{b}+\mathrm{c}}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{and}\:\frac{\mathrm{ac}}{\mathrm{a}+\mathrm{c}}\:=\:\frac{\mathrm{1}}{\mathrm{5}}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{24abc}}{\mathrm{ab}+\mathrm{ac}+\mathrm{bc}}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Let}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{be}\:\mathrm{two}\:\mathrm{real}\:\mathrm{number}\:\mathrm{that} \\ $$$$\mathrm{satisfy}\:\mathrm{p}.\mathrm{q}=\mathrm{2013}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\left(\mathrm{p}+\mathrm{q}\right)^{\mathrm{2}} \:? \\ $$ Answered by…

find-integers-a-gt-b-gt-c-gt-0-such-that-1-a-2-b-3-c-1-

Question Number 181837 by mr W last updated on 01/Dec/22 $${find}\:{integers}\:{a}>{b}>{c}>\mathrm{0}\:{such}\:{that} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{2}}{{b}}+\frac{\mathrm{3}}{{c}}=\mathrm{1} \\ $$ Commented by SEKRET last updated on 01/Dec/22 $$\left(\mathrm{2};\mathrm{5};\mathrm{30}\right)\:\left(\mathrm{2};\mathrm{6};\mathrm{18}\right)\:\left(\mathrm{2};\mathrm{7};\mathrm{14}\right)\:\left(\mathrm{2};\mathrm{8};\mathrm{12}\right) \\ $$$$\left(\mathrm{2};\mathrm{10};\mathrm{10}\right)\:\left(\mathrm{2};\mathrm{12};\mathrm{9}\right)\left(\mathrm{2};\mathrm{16};\mathrm{8}\right)\left(\mathrm{2};\mathrm{28};\mathrm{7}\right)…