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Category: Algebra

Question-211398

Question Number 211398 by Spillover last updated on 08/Sep/24 Answered by Frix last updated on 08/Sep/24 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}}}\:\overset{{t}=\frac{{x}+\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}}}{\:\sqrt{\mathrm{2}}}} {=} \\ $$$$=\mathrm{2}\sqrt{\mathrm{2}}\int\frac{{dt}}{\mathrm{2}{t}^{\mathrm{2}} +\mathrm{1}}=\mathrm{2tan}^{−\mathrm{1}} \:\sqrt{\mathrm{2}}{t}\:= \\…

Question-211402

Question Number 211402 by efronzo1 last updated on 08/Sep/24 Answered by A5T last updated on 08/Sep/24 $${Q}\mathrm{211029},\:{we}\:{can}\:{find}\:{a}\:{polynomial}\:{f}\left({x}\right) \\ $$$${f}\left({x}\right)={x}^{{n}} \underset{−} {+}\mathrm{1} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{28}\Rightarrow{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{1} \\…

Question-211393

Question Number 211393 by BaliramKumar last updated on 08/Sep/24 Commented by BaliramKumar last updated on 08/Sep/24 $${a}^{\mathrm{2}} −{b}^{\mathrm{2}} \:=\:\mathrm{25}\:\:\:\:\:\:\:\:\:\:\:{a}+{b}\:=\:\mathrm{5} \\ $$$$\left({a}−{b}\right)\left({a}+{b}\right)\:=\:\mathrm{25} \\ $$$$\left({a}−{b}\right)\mathrm{5}\:=\:\mathrm{25} \\ $$$${a}−{b}\:=\:\mathrm{5}………\left({i}\right)…

soit-le-systeme-d-equatiins-x-y-z-7-x-2-y-2-z-2-9-xyz-5-1-x-1-y-1-z-

Question Number 211368 by a.lgnaoui last updated on 07/Sep/24 $$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{d}\:\mathrm{equatiins} \\ $$$$\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}\:\:\:\:=\mathrm{7} \\ $$$$\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{9} \\ $$$$\:\:\boldsymbol{\mathrm{xyz}}\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{5} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{z}}}? \\ $$…

Question-211381

Question Number 211381 by Spillover last updated on 07/Sep/24 Commented by MathematicalUser2357 last updated on 10/Sep/24 $$\mathrm{Is}\:\mathrm{it}\:\int_{\mathrm{0}} ^{\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)} \mathrm{sinh}^{\mathrm{3}} {x}\:\mathrm{cosh}^{\mathrm{11}} {x}\:{dx} \\ $$ Answered by…