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Category: Algebra

Eliminate-t-from-this-equation-1-x-1-t-y-1-1-t-2-x-3-t-3-y-2-1-t-

Question Number 49570 by Tawa1 last updated on 07/Dec/18 $$\mathrm{Eliminate}\:\:\boldsymbol{\mathrm{t}}\:\:\mathrm{from}\:\mathrm{this}\:\mathrm{equation}:\:\:\left(\mathrm{1}\right)\:\:\:\mathrm{x}\:=\:\mathrm{1}\:+\:\mathrm{t},\:\:\:\mathrm{y}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{x}\:=\:\mathrm{3}\:+\:\mathrm{t}^{\mathrm{3}} \:,\:\:\:\:\:\mathrm{y}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$ Answered by afachri last updated on 07/Dec/18 $$\left.\mathrm{1}\right)\:\:{t}\:=\:{x}\:−\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\mathrm{so},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:=\:\mathrm{1}\:+\:\frac{\:\mathrm{1}\:}{\:{x}\:−\:\mathrm{1}\:}…

Question-180604

Question Number 180604 by mathlove last updated on 14/Nov/22 Answered by Frix last updated on 14/Nov/22 $${x}=\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}\:^{…} } } =\sqrt{\mathrm{2}}\:^{{x}} \\ $$$$\mathrm{ln}\:{x}\:={x}\mathrm{ln}\:\sqrt{\mathrm{2}} \\ $$$$\frac{\mathrm{ln}\:{x}}{{x}}=\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{2}} \\…

find-the-real-solution-of-following-equation-system-x-2-xy-y-2-p-y-2-yz-z-2-q-z-2-zx-x-2-r-with-p-q-r-gt-0-

Question Number 180603 by mr W last updated on 14/Nov/22 $${find}\:{the}\:{real}\:{solution}\:{of}\:{following} \\ $$$${equation}\:{system}: \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{xy}}+\boldsymbol{{y}}^{\mathrm{2}} =\boldsymbol{{p}} \\ $$$$\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{yz}}+\boldsymbol{{z}}^{\mathrm{2}} =\boldsymbol{{q}} \\ $$$$\boldsymbol{{z}}^{\mathrm{2}} +\boldsymbol{{zx}}+\boldsymbol{{x}}^{\mathrm{2}} =\boldsymbol{{r}}…

x-4-x-1-gt-4x-5-

Question Number 180569 by SAMIRA last updated on 13/Nov/22 $$\sqrt{\boldsymbol{{x}}+\mathrm{4}}\:−\:\sqrt{\boldsymbol{{x}}−\mathrm{1}}\:>\:\sqrt{\mathrm{4}\boldsymbol{{x}}+\mathrm{5}} \\ $$ Commented by Frix last updated on 14/Nov/22 $$\mathrm{false}. \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\geqslant\mathrm{1} \\ $$$$\mathrm{but}\:\mathrm{for}\:{x}\geqslant\mathrm{0}:\:\sqrt{{x}+\mathrm{4}}<\sqrt{\mathrm{4}{x}+\mathrm{5}} \\…

Resoudre-dans-R-1-a-b-c-2-a-2-b-2-c-2-6-1-a-1-b-1-c-1-2-2-x-2-xy-y-2-3-y-2-yz-z-2-7-z-2-zx-x-2-13-

Question Number 180542 by a.lgnaoui last updated on 13/Nov/22 $${Resoudre}\:{dans}\:\mathbb{R} \\ $$$$\left.\mathrm{1}\right) \\ $$$${a}+{b}+{c}=\mathrm{2} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{6} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)…