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Category: Algebra

Question-157797

Question Number 157797 by akolade last updated on 28/Oct/21 Answered by MJS_new last updated on 28/Oct/21 $${x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}=\sqrt{\frac{\mathrm{4}}{\mathrm{4}−{x}^{\mathrm{2}} }−\mathrm{1}} \\ $$$$\mathrm{squaring}\:\mathrm{and}\:\mathrm{transforming} \\ $$$${x}^{\mathrm{10}} −\mathrm{10}{x}^{\mathrm{8}}…

7x-3-mod-18-

Question Number 92255 by jagoll last updated on 05/May/20 $$\mathrm{7x}\:=\:\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{18}\:\right)\: \\ $$ Answered by Rasheed.Sindhi last updated on 05/May/20 $$\mathrm{7}{x}\equiv\mathrm{3}\left({mod}\:\mathrm{18}\right) \\ $$$$\mathrm{7}{x}\equiv\mathrm{3}+\mathrm{18}\left({mod}\:\mathrm{18}\right) \\ $$$$\mathrm{7}{x}\equiv\mathrm{21}\left({mod}\:\mathrm{18}\right) \\…

x-y-y-x-6-x-y-5-find-x-3-1-y-

Question Number 92252 by john santu last updated on 05/May/20 $$\begin{cases}{\mathrm{x}\sqrt{\mathrm{y}}\:+\mathrm{y}\sqrt{\mathrm{x}}\:=\:\mathrm{6}}\\{\mathrm{x}+\mathrm{y}\:=\:\mathrm{5}\:}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{\mathrm{y}}\:=\: \\ $$ Answered by john santu last updated on 05/May/20 Commented…

Question-157790

Question Number 157790 by MathSh last updated on 28/Oct/21 Answered by MJS_new last updated on 28/Oct/21 $$\mathrm{let}\:{c}=\mathrm{cos}\:{x} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{32}{c}^{\mathrm{5}} −\mathrm{40}{c}^{\mathrm{3}} +\mathrm{9}{c}}+\sqrt[{\mathrm{3}}]{\mathrm{16}{c}^{\mathrm{5}} −\mathrm{20}{c}^{\mathrm{3}} +\mathrm{4}{c}}=\sqrt[{\mathrm{3}}]{{c}} \\ $$$${u}+{v}={w}\:\:\:\:\:\mid^{\mathrm{3}}…

Question-157781

Question Number 157781 by amin96 last updated on 27/Oct/21 Answered by mr W last updated on 27/Oct/21 $$\mathrm{100}{A}=\left(\frac{\mathrm{1}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{101}}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{102}}\right)+…+\left(\frac{\mathrm{1}}{\mathrm{25}}−\frac{\mathrm{1}}{\mathrm{125}}\right) \\ $$$$\mathrm{25}{B}=\left(\frac{\mathrm{1}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{26}}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{27}}\right)+…+\left(\frac{\mathrm{1}}{\mathrm{100}}−\frac{\mathrm{1}}{\mathrm{125}}\right) \\ $$$$\mathrm{25}{B}−\mathrm{100}{A}=\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{125}}\right)−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{125}}\right)=\mathrm{0} \\ $$$$\mathrm{25}{B}=\mathrm{100}{A} \\…