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Category: Algebra

Solve-the-inequality-x-3-x-1-2-x-x-3-4-6-7x-2-29x-4-gt-0-Z-A-

Question Number 164269 by Zaynal last updated on 15/Jan/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Solve}}\:\boldsymbol{{the}}\:\boldsymbol{{inequality}}; \\ $$$$\:\:\left(\boldsymbol{{x}}+\mathrm{3}\right)\left[\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} −\boldsymbol{{x}}\left(\boldsymbol{{x}}+\frac{\mathrm{3}}{\mathrm{4}}\right)\right]+\mathrm{6}+\frac{\mathrm{7}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{29}\boldsymbol{{x}}}{\mathrm{4}}>\mathrm{0} \\ $$$$\left\{\boldsymbol{{Z}}.\boldsymbol{{A}}\right\} \\ $$ Answered by manxsolar last updated on 15/Jan/22…

Solve-2-3n-2-7-2-2n-2-31-2-n-8-0-n-R-I-need-some-help-with-this-

Question Number 33200 by pieroo last updated on 12/Apr/18 $$\mathrm{Solve}\:\mathrm{2}^{\mathrm{3n}+\mathrm{2}} \:−\mathrm{7}×\mathrm{2}^{\mathrm{2n}+\mathrm{2}} \:−\mathrm{31}×\mathrm{2}^{\mathrm{n}} \:−\mathrm{8}=\mathrm{0},\:\mathrm{n}\in\boldsymbol{\mathrm{R}}. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{some}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this} \\ $$ Answered by MJS last updated on 12/Apr/18 $$\mathrm{2}^{\mathrm{3}{n}+\mathrm{2}}…

Q-If-is-a-root-of-the-equation-x-3-3x-1-0-prove-that-the-other-roots-are-2-2-and-2-2-Please-help-

Question Number 33193 by SammyKT last updated on 12/Apr/18 $$\mathrm{Q}.\:\:\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{1}=\mathrm{0}, \\ $$$$\:\:\:\:\:\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{other}\:\mathrm{roots}\:\mathrm{are} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}−\alpha^{\mathrm{2}} \:\mathrm{and}\:\alpha^{\mathrm{2}} −\alpha−\mathrm{2}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Please}\:\mathrm{help}. \\ $$ Answered by…

Find-n-1-ln-n-

Question Number 164240 by HongKing last updated on 15/Jan/22 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{ln}\:\left(\mathrm{n}\right)\:=\:? \\ $$ Answered by mathmax by abdo last updated on 15/Jan/22 $$\mathrm{this}\:\mathrm{serie}\:\mathrm{diverges}\:\mathrm{to}\:+\infty \\…

Evalute-the-sum-k-1-n-k-pi-n-2-arctan-kpi-n-2-

Question Number 164196 by HongKing last updated on 15/Jan/22 $$\mathrm{Evalute}\:\mathrm{the}\:\mathrm{sum}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{k}\:\left(\frac{\pi}{\mathrm{n}}\right)^{\mathrm{2}} \mathrm{arctan}\:\left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)^{\mathrm{2}} \\ $$ Answered by mathmax by abdo last updated on…

Question-164193

Question Number 164193 by mathlove last updated on 15/Jan/22 Commented by MJS_new last updated on 15/Jan/22 $${x},\:{y},\:{z}\:\mathrm{can}\:\mathrm{be}\:>\mathrm{0}\:\mathrm{or}\:<\mathrm{0} \\ $$$$\Rightarrow \\ $$$$\mathrm{answer}\:\mathrm{is}\:\mathrm{3}\:\mathrm{or}\:\frac{\mathrm{1}}{\mathrm{300}} \\ $$ Commented by…