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Category: Algebra

Question-158919

Question Number 158919 by quvonnn last updated on 10/Nov/21 Answered by floor(10²Eta[1]) last updated on 10/Nov/21 $$\mathrm{4x}=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\mathrm{4x}}}}=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+…}}}}} \\ $$$$\mathrm{4x}=\sqrt{\mathrm{x}+\mathrm{4x}}=\sqrt{\mathrm{5x}} \\ $$$$\mathrm{16x}^{\mathrm{2}} =\mathrm{5x}\Rightarrow\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\frac{\mathrm{5}}{\mathrm{16}} \\ $$$$ \\…

k-1-2011-1-k-k-1-k-2-

Question Number 93340 by john santu last updated on 12/May/20 $$\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{2011}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)\left(\mathrm{k}+\mathrm{2}\right)}\:? \\ $$ Commented by mathmax by abdo last updated on 12/May/20 $${let}\:{A}_{{n}}…

Question-158843

Question Number 158843 by mnjuly1970 last updated on 09/Nov/21 Commented by mr W last updated on 09/Nov/21 $$\left(\mathrm{1}\right) \\ $$$${not}\:{true}! \\ $$$${example}:\:{x}=\mathrm{4},\:{y}=\mathrm{6} \\ $$$$\mathrm{6}{x}+\mathrm{11}{y}=\mathrm{24}+\mathrm{66}=\mathrm{90}\:\equiv\mathrm{0}\:{mod}\left(\mathrm{30}\right) \\…

4-2a-b-2-a-b-2-

Question Number 27761 by shiv15031973@gmail.com last updated on 14/Jan/18 $$\mathrm{4}\left(\mathrm{2a}+\mathrm{b}\right)^{\mathrm{2}} −\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} \\ $$ Answered by Rasheed.Sindhi last updated on 14/Jan/18 $$\:\:\:\mathrm{4}\left(\mathrm{2a}+\mathrm{b}\right)^{\mathrm{2}} −\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} \\ $$$$=\mathrm{4}\left(\mathrm{4a}^{\mathrm{2}} +\mathrm{4ab}+\mathrm{b}^{\mathrm{2}}…