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Category: Algebra

Question-212152

Question Number 212152 by RojaTaniya last updated on 04/Oct/24 Answered by som(math1967) last updated on 04/Oct/24 $$\:{x}^{\mathrm{3}} +{ax}+{b}=\left({x}+{c}\right)\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right) \\ $$$${put}\:{x}=\mathrm{1} \\ $$$$\:{a}+{b}=−\mathrm{1}\:….{case}\mathrm{1} \\ $$$${put}\:{x}=\mathrm{2} \\…

If-f-x-x-2-4x-3-g-x-7-x-0-x-lt-7-5x-5x-x-7-R-fog-a-b-find-the-value-of-b-a-R

Question Number 212140 by mnjuly1970 last updated on 03/Oct/24 $$ \\ $$$$\:\mathrm{I}{f},\:\:\:\:\:{f}\left({x}\right)=−\:{x}^{\mathrm{2}} \:+\mathrm{4}{x}\:−\mathrm{3}\: \\ $$$$\:\:\:\:\: \\ $$$$,\:{g}\left({x}\right)=\:\begin{cases}{\:\sqrt{\mathrm{7}−{x}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\:<\mathrm{7}}\\{\:\:\lfloor\:\mathrm{5}{x}\:\rfloor\:−\mathrm{5}{x}\:\:\:\:\:\:\:\:{x}\geqslant\mathrm{7}}\end{cases}\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:{R}_{{fog}} \:=\:\left({a}\:,{b}\right]\:\: \\ $$$$\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:\:{b}−{a} \\…

solve-an-equation-ln-x-ln-x-

Question Number 212123 by MrGaster last updated on 02/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{an}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\boldsymbol{\mathrm{ln}}\:\boldsymbol{{x}}}=\boldsymbol{\mathrm{ln}}\sqrt{\boldsymbol{{x}}} \\ $$ Answered by Frix last updated on 02/Oct/24 $$\sqrt{\mathrm{ln}\:{x}}=\frac{\mathrm{ln}\:{x}}{\mathrm{2}} \\…

Prove-that-ln-13-1-10-13-2-gt-0-without-calculator-

Question Number 212098 by CrispyXYZ last updated on 30/Sep/24 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{ln}\:\frac{\sqrt{\mathrm{13}}−\mathrm{1}}{\mathrm{10}}\:+\:\sqrt{\mathrm{13}}\:−\:\mathrm{2}\:>\mathrm{0} \\ $$$$\mathrm{without}\:\mathrm{calculator}. \\ $$ Answered by MrGaster last updated on 03/Nov/24 $$\mathrm{ln}\left(\sqrt{\mathrm{13}}−\mathrm{1}\right)−\mathrm{ln}\:\mathrm{10}+\sqrt{\mathrm{13}}−\mathrm{2}>\mathrm{0} \\…

1-1-2-1-3-1-4-1-1000000-note-6-25-6-0-47-0-

Question Number 212094 by behi834171 last updated on 29/Sep/24 $$\left[\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+…….+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1000000}}}\right]=? \\ $$$$\boldsymbol{{note}}:\:\:\:\left[\mathrm{6}.\mathrm{25}\right]=\mathrm{6}\:\:\:,\left[\mathrm{0}.\mathrm{47}\right]=\mathrm{0} \\ $$ Answered by fabricio2008 last updated on 30/Sep/24 $$\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}^{\mathrm{6}} } {\sum}}\left(\sqrt{{x}}\right)^{-\mathrm{1}}…

Question-212052

Question Number 212052 by Spillover last updated on 28/Sep/24 Answered by Ghisom last updated on 28/Sep/24 $$\int\frac{{dx}}{\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} }= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{M}\:\mathrm{ethod}\right] \\ $$$$=−\frac{{x}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{1}}= \\…

Question-212049

Question Number 212049 by Spillover last updated on 28/Sep/24 Answered by Ghisom last updated on 28/Sep/24 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{dx}}{\:\sqrt{−\mathrm{ln}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{−\mathrm{ln}\:{x}}\right] \\ $$$$=−\mathrm{2}\underset{\infty} {\overset{\mathrm{0}} {\int}}\mathrm{e}^{−{t}^{\mathrm{2}}…