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Question Number 110136 by qwerty111 last updated on 27/Aug/20 Answered by $@y@m last updated on 27/Aug/20 $${Let}\:\mathrm{2020}^{{m}} ={a}\: \\ $$$${Given}, \\ $$$${a}+\frac{\mathrm{1}}{{a}}=\mathrm{3}\:…..\left(\mathrm{1}\right) \\ $$$${Squarring}\:{both}\:{sides}, \\…
Question Number 175653 by mnjuly1970 last updated on 04/Sep/22 $$ \\ $$$$\:\:\:{Q}:\:\:{prove}\:{that}\:{the}\:{following} \\ $$$$\:\:\:\:\:{equation}\:{has}\:{no}\:{solution}. \\ $$$$ \\ $$$$\:\:\:\sqrt{{x}\:+\lfloor\:{x}\:\rfloor}\:+\:\sqrt{{x}\:−\sqrt{{x}}\:}\:=\:\mathrm{1} \\ $$$$ \\ $$ Answered by mahdipoor…
Question Number 44570 by deepakkumardas last updated on 01/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 Commented by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 Commented by…
Question Number 175639 by Linton last updated on 04/Sep/22 $${x}^{\mathrm{99}} +{y}^{\mathrm{99}} =\:{x}^{\mathrm{100}} \\ $$$${Interger}\:{solutions}?\: \\ $$ Answered by BaliramKumar last updated on 04/Sep/22 $${x}^{\mathrm{99}} \left[\mathrm{1}\:+\:\left(\frac{{y}}{{x}}\right)^{\mathrm{99}}…
Question Number 110087 by 1549442205PVT last updated on 27/Aug/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{following}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\begin{cases}{\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{2}}\\{\mathrm{2x}+\mathrm{3y}+\mathrm{z}=\mathrm{1}}\\{\mathrm{x}^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{2}\right)^{\mathrm{2}} +\left(\mathrm{z}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{9}}\end{cases} \\ $$ Commented by bemath last updated on 27/Aug/20 $$\:\:\:\left[\bigtriangleup\frac{{be}}{{math}}\bigtriangledown\right]…
Question Number 175620 by infinityaction last updated on 04/Sep/22 $${the}\:{domain}\:{of}\:\:{f}\left({x}\right)\:\:=\:\:\sqrt{\mathrm{log}_{{x}} \left\{{x}\right\}}\:\:; \\ $$$$\left\{.\right\}\:{denote}\:{the}\:{fractional}\:{part}\:{is} \\ $$ Commented by mahdipoor last updated on 04/Sep/22 $$\left(\mathrm{0},+\infty\right)−\mathrm{N}= \\ $$$$\left(\mathrm{0},\mathrm{1}\right)\cup\left(\mathrm{1},\mathrm{2}\right)\cup\left(\mathrm{2},\mathrm{3}\right)\cup\left(\mathrm{3},\mathrm{4}\right)\cup……
Question Number 44543 by ajfour last updated on 01/Oct/18 $${If}\:\:{y}\:={f}\left({x}\right)\:=\:{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:\:{at}\:{some}\:{x},\:{say}\:\:{x}=\:{p} \\ $$$$\int_{\mathrm{0}} ^{\:\:{p}} {ydx}\:=\:{y}\left({p}\right)=\:{y}\:'\left({p}\right)\:=\:{y}\:''\left({p}\right)=\:{p}\:, \\ $$$${then}\:{find}\:\boldsymbol{{p}}\:. \\ $$ Commented by MrW3 last…
Question Number 175593 by Shrinava last updated on 03/Sep/22 $$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{a}}&{\mathrm{log}\left(\mathrm{a}^{\boldsymbol{\mathrm{a}}} \right)}\\{\mathrm{1}}&{\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}}\:\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{8}}}\:\centerdot\:\mathrm{log}\left(\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}\right)}&{}\\{\mathrm{1}}&{\mathrm{b}}&{\mathrm{log}\left(\mathrm{b}^{\boldsymbol{\mathrm{b}}} \right)}\end{vmatrix}\geqslant\:\mathrm{0} \\ $$ Commented by Rasheed.Sindhi…
Question Number 44502 by Tip Top last updated on 30/Sep/18 $$\mathrm{If}\:\mathrm{a}>\mathrm{b},\mathrm{and}\:\mathrm{c}>\mathrm{d},\mathrm{prove}\:\mathrm{that}\:\mathrm{a}−\mathrm{c}\:\mathrm{may}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than}, \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{or}\:\mathrm{less}\:\mathrm{than}\:\mathrm{b}−\mathrm{d}. \\ $$$$ \\ $$ Answered by MrW3 last updated on 30/Sep/18 $${a}={b}+\delta,\:\delta>\mathrm{0}…