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Category: Algebra

4-2x-2-8-x-

Question Number 29433 by Victor31926 last updated on 08/Feb/18 $$\mathrm{4}\left(\mathrm{2x}^{\mathrm{2}} \right)=\mathrm{8}^{\mathrm{x}} \\ $$ Answered by mrW2 last updated on 08/Feb/18 $$\Rightarrow\mathrm{8}{x}^{\mathrm{2}} =\mathrm{8}^{{x}} \\ $$$$\Rightarrow\left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)^{\mathrm{2}} =\mathrm{8}^{{x}}…

Question-94960

Question Number 94960 by bshahid010@gmail.com last updated on 22/May/20 Answered by Kunal12588 last updated on 22/May/20 $$\mathrm{2}+\left({n}−\mathrm{1}\right)\left(\mathrm{3}\right)=\mathrm{2}+\left({n}_{\mathrm{1}} −\mathrm{1}\right)\left(\mathrm{5}\right) \\ $$$$\Rightarrow\mathrm{3}{n}−\mathrm{1}=\mathrm{5}{n}_{\mathrm{1}} −\mathrm{3} \\ $$$$\Rightarrow\mathrm{5}{n}_{\mathrm{1}} −\mathrm{3}{n}=\mathrm{2} \\…

Question-29424

Question Number 29424 by Tinkutara last updated on 08/Feb/18 Commented by prof Abdo imad last updated on 09/Feb/18 $$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{2}^{{n}} \:{n}!}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)}=\sum_{{n}=\mathrm{1}} ^{\infty} \:{u}_{{n}} \\…

Question-160487

Question Number 160487 by HongKing last updated on 30/Nov/21 Answered by Rasheed.Sindhi last updated on 30/Nov/21 $$\left(\mathrm{10}{a}+{b}\right)+\left(\mathrm{10}{b}+{a}\right)=\mathrm{10}{c}+\mathrm{3} \\ $$$$\mathrm{11}{a}+\mathrm{11}{b}=\mathrm{10}{c}+\mathrm{3} \\ $$$$\mathrm{11}\left({a}+{b}\right)=\mathrm{10}{c}+\mathrm{3}…………..\left({i}\right) \\ $$$$\mathrm{11}\mid\:\mathrm{10}{c}+\mathrm{3}\Rightarrow\mathrm{10}{c}+\mathrm{3}=\mathrm{33}\Rightarrow{c}=\mathrm{3} \\ $$$$\left(\mathrm{2}-{digit}\:{multiple}\:{of}\:\mathrm{11}\:{with}\:{unit}\:\mathrm{3}\right.…

Question-160473

Question Number 160473 by quvonnn last updated on 30/Nov/21 Answered by Rasheed.Sindhi last updated on 30/Nov/21 $$ \\ $$$${a}+{b}>{c}\:\wedge\:{b}+{c}>{a}\:\wedge\:{c}+{a}>{b} \\ $$$${a}+{b}−{c}>\mathrm{0}\:\wedge\:{b}+{c}−{a}>\mathrm{0}\:\wedge\:{c}+{a}−{b}>\mathrm{0} \\ $$$$\sqrt{{a}+{b}−{c}}\:\leqslant\sqrt{{a}}\:+\sqrt{{b}}\:−\sqrt{{c}} \\ $$$$\frac{\sqrt{{a}+{b}−{c}}\:}{\:\sqrt{{a}}\:+\sqrt{{b}}\:−\sqrt{{c}}}\leqslant\mathrm{1}……………..\left({i}\right)…

Simplfy-1-cos-sin-2-1-1-cos-sin-2-

Question Number 160457 by HongKing last updated on 29/Nov/21 $$\mathrm{Simplfy}: \\ $$$$\frac{\mathrm{1}\:+\:\mathrm{cos}\boldsymbol{\alpha}}{\mathrm{sin}^{\mathrm{2}} \boldsymbol{\alpha}}\::\:\left(\mathrm{1}\:+\:\left(\frac{\mathrm{1}\:+\:\mathrm{cos}\boldsymbol{\alpha}}{\mathrm{sin}\boldsymbol{\alpha}}\right)^{\mathrm{2}} \right) \\ $$ Answered by MJS_new last updated on 29/Nov/21 $$\frac{\frac{\mathrm{1}+{c}}{{s}^{\mathrm{2}} }}{\mathrm{1}+\left(\frac{\mathrm{1}+{c}}{{s}}\right)^{\mathrm{2}}…