Question Number 198849 by sonukgindia last updated on 25/Oct/23 Commented by mr W last updated on 25/Oct/23 $${for}\:{a},{b},\:{c}\:\in{R}\:{no}\:{solution}! \\ $$ Answered by AST last updated…
Question Number 198850 by mustafazaheen last updated on 25/Oct/23 $$ \\ $$$$\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$$$ \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last…
Question Number 198851 by Tawa11 last updated on 25/Oct/23 You want to arrange 17 books on the shelf of a bookstore. The shelf is dedicated…
Question Number 198813 by mnjuly1970 last updated on 24/Oct/23 $$ \\ $$$$\:\:\:\:\:{suppose}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:{E}=\:\sqrt{\:\mathrm{9}\:+\:\mathrm{4}\:\left(\:\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\:{a}_{\:{k}} ^{\:\mathrm{2}} \:\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{is}\:\:{given} \\ $$$$\:\:\:\:\:{let}\:\:\:\:{a}_{\:{k}} \:=\:{a}_{{k}−\mathrm{1}}…
Question Number 198814 by hardmath last updated on 24/Oct/23 $$\mathrm{Simplify}: \\ $$$$\frac{\left(\sqrt{\mathrm{x}\:+\:\mathrm{4}\:\sqrt{\mathrm{x}\:-\:\mathrm{4}}}\:+\:\sqrt{\mathrm{x}\:-\:\mathrm{4}\:\sqrt{\mathrm{x}\:-\:\mathrm{4}}}\right)\:\sqrt{\mathrm{x}\:-\:\mathrm{8}}}{\mathrm{4}\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{12x}\:+\:\mathrm{32}}} \\ $$ Answered by a.lgnaoui last updated on 24/Oct/23 $$=\frac{\mathrm{1}}{\mathrm{4}}\sqrt{\frac{\mathrm{x}+\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}{\boldsymbol{\mathrm{x}}−\mathrm{4}}}\:+\frac{\mathrm{1}}{\mathrm{4}}\sqrt{\frac{\boldsymbol{\mathrm{x}}−\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}{\boldsymbol{\mathrm{x}}−\mathrm{4}}} \\ $$$$=\frac{\sqrt{\boldsymbol{\mathrm{x}}+\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}\:}\:+\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}}{\:\mathrm{4}\sqrt{\boldsymbol{\mathrm{x}}−\mathrm{4}}}…
Question Number 198750 by depressiveshrek last updated on 24/Oct/23 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tautology}: \\ $$$$\left[\left({p}\veebar{q}\right)\wedge\left({p}\Rightarrow{r}\right)\right]\Rightarrow\left({q}\veebar{r}\right) \\ $$ Answered by MathematicalUser2357 last updated on 29/Dec/23 $$\mathrm{Only}\:\mathrm{know}\:\mathrm{until} \\ $$$$=\sim\left[\left({p}\veebar{q}\right)\wedge\left(\sim{p}\vee{r}\right)\right]\vee\left({q}\veebar{r}\right) \\…
Question Number 198815 by a.lgnaoui last updated on 24/Oct/23 $$\mathrm{Determiner}\:\boldsymbol{\mathrm{x}} \\ $$ Commented by a.lgnaoui last updated on 24/Oct/23 Commented by cherokeesay last updated on…
Question Number 198809 by dimentri last updated on 24/Oct/23 $$\:\:\:\:\:{sum}\:{of}\:{roots}\: \\ $$$$\:\mathrm{log}\:_{\mathrm{3}} {x}\:+\:\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2},\mathrm{5}\right)\:+\:\mathrm{log}\:_{{x}} \mathrm{9}\:=\:\mathrm{3}+\:\mathrm{log}\:_{{x}} \mathrm{5}\: \\ $$ Answered by a.lgnaoui last updated on 24/Oct/23…
Question Number 198772 by ajfour last updated on 24/Oct/23 $${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$ Commented by Frix last updated on 24/Oct/23 $$\mathrm{Usually}\:\mathrm{we}\:\mathrm{first}\:\mathrm{try}\:\mathrm{factors}\:\mathrm{of}\:{d}.\:\mathrm{The}\:\mathrm{next} \\ $$$$\mathrm{step}\:\mathrm{would}\:\mathrm{be}\:\mathrm{substituting}\:{x}={t}−\frac{{a}}{\mathrm{4}}\:\mathrm{to}…
Question Number 198806 by sonukgindia last updated on 24/Oct/23 Answered by Frix last updated on 24/Oct/23 $$\int\frac{\mathrm{7}{x}^{\mathrm{2}} +\mathrm{5}}{{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{25}}{dx}= \\ $$$$=\int\left(\frac{\mathrm{3}{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}\right)}−\frac{\mathrm{3}{x}−\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\right)}\right){dx}= \\…