Question Number 170491 by jahar last updated on 25/May/22 $$\left.\mathrm{1}\right)\:{Help} \\ $$$$\mathrm{5}^{{x}} −\mathrm{3}^{{x}} =\mathrm{9}\: \\ $$ Answered by MathsFan last updated on 25/May/22 $${let}\:{f}\left({x}\right)=\mathrm{5}^{{x}} −\mathrm{3}^{{x}}…
Question Number 170478 by balirampatel last updated on 24/May/22 $$\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} \\ $$$$\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:+\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:={a} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:+\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:}\centerdot\frac{\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:−\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:}{\:\sqrt[{\mathrm{3}}]{\:\mathrm{9}\:−\:\mathrm{4}\sqrt{\mathrm{5}}\:}\:} \\…
Question Number 170427 by mathlove last updated on 23/May/22 $$\mathrm{14}^{{b}} =\mathrm{7}^{{b}−{a}} \\ $$$$\mathrm{49}^{\frac{{a}}{{b}}} =? \\ $$ Answered by thfchristopher last updated on 23/May/22 $$\mathrm{14}^{{b}} =\mathrm{7}^{{b}−{a}}…
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Question Number 39332 by abdo mathsup 649 cc last updated on 05/Jul/18 $$\left.\mathrm{1}\right)\:{simplify}\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}^{\mathrm{2}} \left({kx}\right) \\ $$$$\left.\mathrm{2}\right){simplify}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}^{\mathrm{2}} \left(\frac{{k}\pi}{{n}}\right) \\ $$…
Question Number 104859 by qwertyu last updated on 24/Jul/20 Answered by Dwaipayan Shikari last updated on 24/Jul/20 $${S}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{4}}{\mathrm{2}^{\mathrm{4}} }+….+\frac{{n}}{\mathrm{2}^{{n}} } \\ $$$$\frac{{S}_{{n}}…
Question Number 170389 by mr W last updated on 22/May/22 $${solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{3}} +\sqrt[{\mathrm{3}}]{\mathrm{3}−{x}}−\mathrm{3}=\mathrm{0} \\ $$ Commented by Mastermind last updated on 22/May/22 $${We}\:{can}\:{actually}\:{solve}\:{this}\:{by}\:{graph} \\…
Question Number 104832 by bemath last updated on 24/Jul/20 $$\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}}…
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