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Category: Algebra

Solve-diopthantine-equation-1-a-1-b-2-17-

Question Number 128636 by john_santu last updated on 09/Jan/21 $$\mathrm{Solve}\:\mathrm{diopthantine}\:\mathrm{equation}\: \\ $$$$\:\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}\:=\:\frac{\mathrm{2}}{\mathrm{17}}. \\ $$ Answered by liberty last updated on 09/Jan/21 $$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}=\frac{\mathrm{2}}{\mathrm{17}}\:;\:\mathrm{2ab}\:=\:\mathrm{17}\left(\mathrm{a}+\mathrm{b}\right) \\ $$$$\mathrm{consider}\:\left(\mathrm{2a}−\mathrm{17}\right)\left(\mathrm{2b}−\mathrm{17}\right)=\mathrm{4ab}−\mathrm{34}\left(\mathrm{a}+\mathrm{b}\right)+\mathrm{17}^{\mathrm{2}} \\…

Question-63095

Question Number 63095 by aliesam last updated on 28/Jun/19 Answered by MJS last updated on 29/Jun/19 $$\sqrt[{\mathrm{3}}]{\mathrm{4}{x}^{\mathrm{4}} −\mathrm{40}{x}^{\mathrm{2}} +\mathrm{100}}−\sqrt[{\mathrm{3}}]{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{10}}=\mathrm{20}−\mathrm{2}{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} ={s} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{4}{s}^{\mathrm{2}}…

s-a-2-a-2-d-2-b-a-2-b-2-a-2-2-b-2-c-b-2-2-c-d-p-a-a-2-d-a-b-b-2-a-2-b-c-b-2-Find-a-b-c-or-d-in-terms-of-s-if-p-is-maxim

Question Number 63090 by ajfour last updated on 28/Jun/19 $${s}=\sqrt{{a}^{\mathrm{2}} +\left({a}^{\mathrm{2}} −{d}\right)^{\mathrm{2}} }+\sqrt{\left({b}−{a}\right)^{\mathrm{2}} +\left({b}^{\mathrm{2}} −{a}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\sqrt{{b}^{\mathrm{2}} +\left({c}−{b}^{\mathrm{2}} \right)^{\mathrm{2}} }+{c}−{d} \\ $$$$\:{p}=\:{a}\left({a}^{\mathrm{2}} −{d}\right)+\left({a}+{b}\right)\left({b}^{\mathrm{2}}…

nice-calculus-a-R-amp-a-a-a-2-17a-16-a-

Question Number 128589 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{a}\in\mathbb{R}^{+} \:\: \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\&\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\right\}\Rightarrow\:\sqrt{{a}−\sqrt{{a}}\:}\:=? \\ $$$$\:\:\:\:\:{a}^{\mathrm{2}} −\mathrm{17}{a}=\mathrm{16}\sqrt{{a}}\: \\ $$$$\:\:\:\:\:\:\: \\ $$ Answered by snipers237…

Solve-for-x-5-x-6x-7-

Question Number 62998 by mr W last updated on 27/Jun/19 $${Solve}\:{for}\:{x}:\:\:\mathrm{5}^{\boldsymbol{{x}}} +\mathrm{6}\boldsymbol{{x}}=\mathrm{7} \\ $$ Commented by mr W last updated on 27/Jun/19 $${Equation}\:{like}\:{this}\:{can}\:{be}\:{solved}\:{using} \\ $$$${Lambert}\:{W}\:{function}\:{as}\:{following}:…