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Category: Algebra

Question-77067

Question Number 77067 by Boyka last updated on 03/Jan/20 Commented by Boyka last updated on 03/Jan/20 $$\left[\mathrm{x}\right]−\mathrm{whole}\:\mathrm{part}\:\: \\ $$$$\boldsymbol{\mathrm{x}}=\left[\boldsymbol{\mathrm{x}}\right]+\left\{\boldsymbol{\mathrm{x}}\right\} \\ $$ Commented by mr W…

Question-142607

Question Number 142607 by mathdanisur last updated on 02/Jun/21 Answered by mr W last updated on 03/Jun/21 $${A}_{{max}} =\mathrm{10}^{\mathrm{3}} +\mathrm{5}^{\mathrm{3}} +\mathrm{10}×\mathrm{5}=\mathrm{1175} \\ $$$${A}_{{min}} =−\mathrm{10}^{\mathrm{3}} −\mathrm{5}^{\mathrm{3}}…

4-x-x-1-5-4-6x-x-1-5-1-x-1-x-2-

Question Number 11515 by @ANTARES_VY last updated on 27/Mar/17 $$\sqrt[{\mathrm{5}}]{\frac{\mathrm{4}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}−\sqrt[{\mathrm{5}}]{\frac{\mathrm{4}−\mathrm{6}\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}=\mathrm{1}. \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} +\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$ Answered by ajfour last updated on 27/Mar/17 $$\mathrm{x}=\frac{\mathrm{4}}{\mathrm{15}} \\…

Let-a-b-c-0-and-a-b-c-1-Prove-that-1-a-2-1-1-b-2-1-1-c-2-1-5-2-

Question Number 142577 by loveineq last updated on 02/Jun/21 $$\mathrm{Let}\:{a},{b},{c}\:\geqslant\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{1}.\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{1}}{{b}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{1}}{{c}^{\mathrm{2}} +\mathrm{1}}\:\geqslant\:\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by ajfour last updated on…

z-4-12z-3-0-z-

Question Number 142582 by mathdanisur last updated on 02/Jun/21 $$\boldsymbol{{z}}^{\mathrm{4}} \:+\:\mathrm{12}\boldsymbol{{z}}\:+\:\mathrm{3}\:=\:\mathrm{0}\:\left(\boldsymbol{{z}}=?\right) \\ $$ Answered by ajfour last updated on 02/Jun/21 $$\left({z}^{\mathrm{2}} +{pz}+{q}\right)\left({z}^{\mathrm{2}} −{pz}+\frac{\mathrm{3}}{{q}}\right)=\mathrm{0} \\ $$$$\Rightarrow…

x-2-x-4-x-2-x-4-9-find-the-equation-has-multiple-roots-

Question Number 11500 by @ANTARES_VY last updated on 27/Mar/17 $$\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{4}\right)\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{4}\right)=\mathrm{9} \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}\:\:\boldsymbol{\mathrm{has}}\:\:\boldsymbol{\mathrm{multiple}}\:\:\boldsymbol{\mathrm{roots}}. \\ $$ Answered by ridwan balatif last updated on 27/Mar/17 $$\left(\left(\mathrm{x}^{\mathrm{2}}…

4x-2-7x-5-5x-2-13x-3-3x-x-2-8-0-find-all-the-multiples-of-the-real-roots-of-the-equation-

Question Number 11501 by @ANTARES_VY last updated on 27/Mar/17 $$\left(\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{7}\boldsymbol{\mathrm{x}}−\mathrm{5}\right)\left(\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{13}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)\left(\mathrm{3}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{8}\right)=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{all}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{multiples}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{real}}\:\:\boldsymbol{\mathrm{roots}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equation}}. \\ $$ Commented by mrW1 last updated on…