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Category: Algebra

if-x-gt-0-r-pq-1-p-q-then-1-rx-1-qx-p-1-px-q-1-x-r-

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Question Number 144095 by mathdanisur last updated on 21/Jun/21 $${if}\:\:{x}>\mathrm{0}\:,\:{r}={pq}\:,\:\mathrm{1}\leqslant{p}\leqslant{q}\:\:{then}: \\ $$$$\mathrm{1}+{rx}\:\leqslant\:\left(\mathrm{1}+{qx}\right)^{\boldsymbol{{p}}} \:\leqslant\:\left(\mathrm{1}+{px}\right)^{\boldsymbol{{q}}} \:\leqslant\:\left(\mathrm{1}+{x}\right)^{\boldsymbol{{r}}} \\ $$ Answered by mitica last updated on 21/Jun/21 $$\left(\mathrm{1}+{x}\right)^{{r}} =\left[\left(\mathrm{1}+{x}\right)^{{p}}…

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Is-the-sequence-u-n-defined-by-the-formula-u-n-n-1-5-n-lgn-where-n-Z-n-2-convergent-If-so-find-its-sum-as-n-

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Question Number 408 by 112358 last updated on 30/Dec/14 $${Is}\:{the}\:{sequence}\:\left\{{u}_{{n}} \right\}\:{defined}\:{by}\:{the}\:{formula}\:{u}_{{n}} =\frac{{n}+\left(−\mathrm{1}.\mathrm{5}\right)^{{n}} }{{lgn}}\:,\:{where}\:{n}\in{Z}^{+} \mid{n}\geqslant\mathrm{2}\:,\:{convergent}?\:{If}\:{so}\:{find}\:{its}\:{sum}\:{as}\:{n}\rightarrow\infty. \\ $$ Commented by 123456 last updated on 30/Dec/14 $${u}_{{n}} =\frac{{n}+\left(−\mathrm{1}.\mathrm{5}\right)^{{n}}…

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Question-65911

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Question Number 65911 by Masumsiddiqui399@gmail.com last updated on 05/Aug/19 Commented by Prithwish sen last updated on 06/Aug/19 $$\mathrm{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)=\mathrm{180}×\mathrm{182} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{12}×\mathrm{13}×\mathrm{14}×\mathrm{15} \\ $$$$\because\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number} \\ $$$$\therefore\left(\mathrm{x}+\mathrm{3}\right)=\mathrm{15} \\…

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2x-7-lt-2-solve-

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Question Number 131440 by Study last updated on 04/Feb/21 $$\mid\mathrm{2}{x}+\mathrm{7}\mid<−\mathrm{2}\:\:\:\:\:\:{solve}=? \\ $$ Commented by Dwaipayan Shikari last updated on 04/Feb/21 $${No}\:{solution}\: \\ $$$$\mid{f}\left({x}\right)\mid\geqslant\mathrm{0}\:\:\left({Always}\right) \\ $$…

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If-and-are-roots-of-the-equation-x-3-px-q-0-p-0-q-0-then-find-the-value-of-the-determinant-determinant-

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Question Number 363 by rajabhay last updated on 25/Jan/15 $$\mathrm{If}\:\alpha,\:\beta\:\mathrm{and}\:\gamma\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{3}} +{px}+{q}=\mathrm{0},\:{p}\neq\mathrm{0},\:{q}\neq\mathrm{0}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{determinant}. \\ $$$$\begin{vmatrix}{\alpha}&{\beta}&{\gamma}\\{\beta}&{\gamma}&{\alpha}\\{\gamma}&{\alpha}&{\beta}\end{vmatrix} \\ $$ Commented by 123456 last updated on…

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x-x-x-1-1-x-1-1-x-4-find-x-

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Question Number 131430 by mathlove last updated on 04/Feb/21 $$\sqrt[{\frac{\mathrm{1}}{{x}}}]{\left(\sqrt[{\frac{\mathrm{1}}{{x}}}]{\left.{x}\:^{{x}} \right)^{{x}} }\right.}=\mathrm{4}\:\:\:\:\:\:\:{find}\:\:{x}=? \\ $$ Commented by math35 last updated on 04/Feb/21 $$\sqrt[{\frac{\mathrm{1}}{{x}}}]{\left(\sqrt[{\frac{\mathrm{1}}{{x}}}]{{x}^{{x}^{\mathrm{2}} } }\right.}=\mathrm{4} \\…

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