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Category: Algebra

x-4-15x-2-30x-104-0-for-x-R-x-2-4-I-want-to-know-the-best-way-to-arrive-at-these-answers-without-guessing-I-found-one-new-way-Shall-post-later-

Question Number 201796 by ajfour last updated on 12/Dec/23 $${x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{2}} −\mathrm{30}{x}+\mathrm{104}=\mathrm{0} \\ $$$${for}\:{x}\in\mathbb{R}\:\:\:\:\:{x}=\mathrm{2},\:\mathrm{4} \\ $$$${I}\:{want}\:{to}\:{know}\:{the}\:{best}\:{way}\:{to} \\ $$$${arrive}\:{at}\:{these}\:{answers}\:\left({without}\right. \\ $$$$\left.{guessing}\right).\:{I}\:{found}\:{one}\:{new}\:{way}. \\ $$$$\:{Shall}\:{post}\:{later}. \\ $$ Commented…

Find-the-differential-of-the-function-y-x-2-1-

Question Number 201798 by hardmath last updated on 12/Dec/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\boldsymbol{\mathrm{y}}\:=\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$ Answered by dimentri last updated on 12/Dec/23 $$\:{y}=\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\Rightarrow{y}'=\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}=\frac{{x}}{{y}}…

1-y-tgx-ctgx-y-2-y-1-x-2-arctgx-y-3-y-cos-4-x-y-4-x-2t-y-3t-2-5t-x-y-

Question Number 201764 by hardmath last updated on 11/Dec/23 $$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{tgx}\:−\:\mathrm{ctgx}\:\:\rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{2}.\:\mathrm{y}\:=\:\left(\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{arctgx}\:\rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{3}.\:\mathrm{y}\:=\:\mathrm{cos}^{\mathrm{4}} \:\mathrm{x}\:\rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{4}.\:\begin{cases}{\mathrm{x}\:=\:\mathrm{2t}}\\{\mathrm{y}\:=\:\mathrm{3t}^{\mathrm{2}} \:−\:\mathrm{5t}}\end{cases}\:\:\:\rightarrow\:\:\:\mathrm{x}^{'} \:,\:\mathrm{y}^{'} \:=\:? \\…

cos-2-4x-sin-2-4x-0-25-for-equation-0-90-how-many-roots-are-there-in-the-piece-

Question Number 201728 by hardmath last updated on 11/Dec/23 $$\mathrm{cos}^{\mathrm{2}} \:\mathrm{4x}\:\centerdot\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{4x}\:=\:\mathrm{0},\mathrm{25}\:\mathrm{for}\:\mathrm{equation} \\ $$$$\left[\mathrm{0};\mathrm{90}\right]\:\mathrm{how}\:\mathrm{many}\:\mathrm{roots}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{piece}? \\ $$ Answered by esmaeil last updated on 11/Dec/23…

Find-1-cos3x-cosx-dx-2-3-x-sinx-dx-3-0-1-x-e-x-dx-4-1-e-ln-2-x-dx-

Question Number 201763 by hardmath last updated on 11/Dec/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\int\:\mathrm{cos3x}\:\mathrm{cosx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{2}.\:\int\:\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:\mathrm{sinx}\:\mathrm{dx}\:=\:? \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \:\mathrm{x}\:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$$$\mathrm{4}.\:\int_{\mathrm{1}} ^{\:\boldsymbol{\mathrm{e}}} \:\mathrm{ln}^{\mathrm{2}} \:\mathrm{x}\:\mathrm{dx}\:=\:?…

Question-201689

Question Number 201689 by cherokeesay last updated on 10/Dec/23 Answered by witcher3 last updated on 10/Dec/23 $$\mathrm{x}^{\mathrm{3}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{12x}−\mathrm{32}=\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{3}} −\mathrm{24} \\ $$$$\mathrm{x}−\mathrm{2}=\mathrm{y} \\ $$$$\Leftrightarrow\sqrt[{\mathrm{3}}]{\mathrm{y}+\mathrm{24}}=\mathrm{y}^{\mathrm{3}} −\mathrm{24}…