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Category: Algebra

9-4-5-1-3-9-4-5-1-3-

Question Number 170478 by balirampatel last updated on 24/May/22 $$\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:+\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:−\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 24/May/22 $$\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:+\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:+\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:−\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:={x}\left({say}\right);{x}\in\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:+\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:={a} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:+\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:}\centerdot\frac{\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:−\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:}{\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:−\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:} \\…

Question-104859

Question Number 104859 by qwertyu last updated on 24/Jul/20 Answered by Dwaipayan Shikari last updated on 24/Jul/20 $${S}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{4}}{\mathrm{2}^{\mathrm{4}} }+….+\frac{{n}}{\mathrm{2}^{{n}} } \\ $$$$\frac{{S}_{{n}}…

x-y-x-2-y-2-7-x-y-x-2-y-2-12-

Question Number 104832 by bemath last updated on 24/Jul/20 $$\begin{cases}{{x}+{y}+\frac{{x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:=\:\mathrm{7}}\\{\frac{\left({x}−{y}\right){x}^{\mathrm{2}} }{{y}^{\mathrm{2}} }\:=\:\mathrm{12}\:}\end{cases} \\ $$ Answered by john santu last updated on 24/Jul/20 $${let}\:{x}\:=\:\lambda{y}\:\rightarrow\begin{cases}{\lambda{y}+{y}+\frac{\lambda^{\mathrm{2}}…