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Category: Algebra

2x-x-1-2-8x-1-x-

Question Number 170849 by mathlove last updated on 01/Jun/22 $$\mathrm{2}{x}+\sqrt{{x}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{8}{x}+\frac{\mathrm{1}}{\:\sqrt{{x}}}=? \\ $$ Answered by MJS_new last updated on 01/Jun/22 $$\sqrt{{x}}\in\mathbb{R}\:\Rightarrow\:{x}\leqslant\mathrm{0} \\ $$$$\mathrm{let}\:\sqrt{{x}}={t}\geqslant\mathrm{0} \\…

1-2-2-1-3-2-2-3-1-4-3-3-4-1-100-99-99-100-

Question Number 105306 by bobhans last updated on 27/Jul/20 $$\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}\:}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+…+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$ Commented by bemath last updated on 28/Jul/20 $$\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{1}}+\mathrm{1}\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+…+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$$${a}_{{n}} \:=\:\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\sqrt{{n}}+{n}\sqrt{{n}+\mathrm{1}}}\:=\:\frac{\mathrm{1}}{\:\sqrt{{n}+\mathrm{1}}\left(\sqrt{{n}^{\mathrm{2}} +{n}}+{n}\right)} \\…

x-3-2x-2-5x-6-0-3-3-3-

Question Number 170836 by balirampatel last updated on 01/Jun/22 $${x}^{\mathrm{3}} \:−\:\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{5}{x}\:+\:\mathrm{6}\:=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \:+\:\gamma^{\mathrm{3}} \:=\:? \\ $$ Commented by cortano1 last updated on 01/Jun/22 $$\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}}…

Without-using-tables-or-calculator-compare-6-7-and-7-6-

Question Number 105301 by Don08q last updated on 27/Jul/20 $$\mathrm{Without}\:\mathrm{using}\:\mathrm{tables}\:\mathrm{or}\:\mathrm{calculator}, \\ $$$$\:{compare}\:\:\:\mathrm{6}^{\mathrm{7}} \:\mathrm{and}\:\:\:\mathrm{7}^{\mathrm{6}} \\ $$ Answered by 1549442205PVT last updated on 28/Jul/20 $$\frac{\mathrm{6}^{\mathrm{7}} }{\mathrm{7}^{\mathrm{6}} }=\mathrm{6}×\left(\frac{\mathrm{6}}{\mathrm{7}}\right)^{\mathrm{6}}…

Question-170832

Question Number 170832 by Shrinava last updated on 01/Jun/22 Commented by mr W last updated on 01/Jun/22 $${T}={AM}+{BN}\geqslant\sqrt{{AB}^{\mathrm{2}} +{MN}^{\mathrm{2}} }=\sqrt{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }=\sqrt{\mathrm{34}} \\…

Question-170738

Question Number 170738 by Tawa11 last updated on 30/May/22 Commented by Tawa11 last updated on 30/May/22 $$\mathrm{How}\:\mathrm{to}\:\mathrm{get}\:\mathrm{the}\:\mathrm{second}\:\mathrm{step}\:\mathrm{please}???? \\ $$$$\mathrm{S}\:\:\:=\:\:\:\frac{\mathrm{1}}{\mathrm{8}}\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{3}}{\left(\mathrm{3n}\:+\:\mathrm{1}\right)\left(\mathrm{3n}\:+\:\mathrm{2}\right)}\:\:−\:\:\frac{\mathrm{5}}{\left(\mathrm{3n}\:+\:\mathrm{2}\right)\left(\mathrm{3n}\:+\:\mathrm{3}\right)}\:\:+\:\:\frac{\mathrm{2}}{\left(\mathrm{3n}\:+\:\mathrm{3}\right)\left(\mathrm{3n}\:+\:\mathrm{1}\right)} \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{question}\:… \\ $$…