Question Number 170568 by mathlove last updated on 27/May/22 Answered by Rasheed.Sindhi last updated on 27/May/22 $$\begin{array}{|c|}{\underset{\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{g}\left(\mathrm{2x}+\mathrm{1}\right)=\mathrm{2x}\:\:\:\:\:\:\:\:\:\:} {\mathrm{f}\left(\mathrm{2x}+\mathrm{2}\right)+\mathrm{2g}\left(\mathrm{4x}+\mathrm{7}\right)=\mathrm{x}−\mathrm{1}}}\\\hline\end{array} \\ $$$$\left(\mathrm{1}\right):\:\:\:\:\mathrm{2x}+\mathrm{2}=\mathrm{y}\Rightarrow\mathrm{x}=\frac{\mathrm{y}−\mathrm{2}}{\mathrm{2}}\:: \\ $$$$\:\:\:\:\mathrm{f}\left(\mathrm{y}\right)+\mathrm{2g}\left(\mathrm{4}\centerdot\frac{\mathrm{y}−\mathrm{2}}{\mathrm{2}}+\mathrm{7}\right)=\frac{\mathrm{y}−\mathrm{2}}{\mathrm{2}}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\Rightarrow\mathrm{f}\left(\mathrm{y}\right)+\mathrm{2g}\left(\mathrm{2y}+\mathrm{3}\right)=\frac{\mathrm{y}−\mathrm{4}}{\mathrm{2}}…\left(\mathrm{3}\right) \\…
Question Number 105023 by bemath last updated on 25/Jul/20 $$\frac{\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)^{\mathrm{2}} }{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\left({y}^{\mathrm{2}} −\mathrm{1}\right)}+\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\left({y}^{\mathrm{2}} −\mathrm{1}\right)}+\frac{\left({y}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} }{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)}=…
Question Number 170515 by Tawa11 last updated on 25/May/22 8 men and 12 women can complete a certain job for 6 days. The men work…
Question Number 104973 by malwaan last updated on 25/Jul/20 $$\mathrm{2}\sqrt{\mathrm{3}}\:+\:\boldsymbol{{i}}\:\:\:{is}\:{a}\:{cubic}\:{root}\:{for} \\ $$$$\mathrm{18}\sqrt{\mathrm{3}}\:+\:\mathrm{35}\boldsymbol{{i}}\: \\ $$$$\boldsymbol{{find}}\:\:\boldsymbol{{the}}\:\boldsymbol{{other}}\:\mathrm{2}\:\boldsymbol{{cubic}}\:\boldsymbol{{roots}} \\ $$ Commented by malwaan last updated on 25/Jul/20 شكرا جزيلا سيدي الفاضل واذا كان لديك طريقة او لوحة مفاتيح لكتابة المعادلات والنهايات والتكاملات وغيرها باللغة العربية فاتمنى تساعدني مع فائق احترامي محمد علوان اليمن Answered…
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) \\ $$$$\left.\mathrm{2}\right){simplify}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}^{\mathrm{2}} \left(\frac{{k}\pi}{{n}}\right) \\ $$…