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Category: Algebra

Find-x-x-2-200-x-

Question Number 215350 by hardmath last updated on 03/Jan/25 $$\mathrm{Find}:\:\:\:\mathrm{x}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{2}^{\sqrt{\mathrm{200}}} \:\:\Rightarrow\:\:\mathrm{x}\:=\:? \\ $$ Answered by zetamaths last updated on 03/Jan/25 $$.{is}\:{just}\:{the}\:{lambert}\:{function} \\ $$$${x}^{{x}} =\mathrm{2}^{\sqrt{\mathrm{200}}}…

Show-that-x-64-and-y-729-x-1-3-y-1-3-13-x-y-35-

Question Number 215282 by arkanmathematics63 last updated on 02/Jan/25 $${Show}\:{that}\:{x}=\mathrm{64}\:{and}\:{y}=\mathrm{729}\: \\ $$$$\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}=\mathrm{13} \\ $$$$\sqrt{{x}}+\sqrt{{y}}=\mathrm{35} \\ $$ Commented by Ghisom last updated on 02/Jan/25 $$\mathrm{to}\:“\mathrm{show}\:\mathrm{that}\:{x}=\mathrm{64}\:\mathrm{and}\:{y}=\mathrm{729}''\:\mathrm{it}'\mathrm{s}\:\mathrm{enough} \\…

10-7-9-4-21-8-

Question Number 215248 by sudipyt44 last updated on 01/Jan/25 $$\frac{\mathrm{10}}{\mathrm{7}}\boldsymbol{\div}\frac{\mathrm{9}}{\mathrm{4}}×\frac{\mathrm{21}}{\mathrm{8}} \\ $$ Commented by A5T last updated on 01/Jan/25 $$\left(\mathrm{a}\boldsymbol{\div}\mathrm{b}\right)×\mathrm{c}=\frac{\mathrm{ac}}{\mathrm{b}} \\ $$$$\mathrm{a}\boldsymbol{\div}\left(\mathrm{b}×\mathrm{c}\right)=\frac{\mathrm{a}}{\mathrm{bc}} \\ $$ Answered…

x-2-y-31-y-2-x-41-x-y-

Question Number 215180 by hardmath last updated on 30/Dec/24 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{31}}\\{\mathrm{y}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:=\:\:\mathrm{41}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\left(\mathrm{x}\:;\:\mathrm{y}\right)\:=\:? \\ $$ Commented by Ghisom last updated on 31/Dec/24 $$\mathrm{obviously} \\ $$$$\mathrm{5}^{\mathrm{2}} +\mathrm{6}=\mathrm{31}…

If-ab-ba-n-2-Find-max-a-b-min-a-b-

Question Number 215137 by hardmath last updated on 29/Dec/24 $$\mathrm{If}\:\:\:\overline {\mathrm{ab}}\:+\:\overline {\mathrm{ba}}\:=\:\mathrm{n}^{\mathrm{2}} \\ $$$$\mathrm{Find}\:\:\:\mathrm{max}\left(\mathrm{a}\centerdot\mathrm{b}\right)\:−\:\mathrm{min}\left(\mathrm{a}\centerdot\mathrm{b}\right)\:=\:? \\ $$ Answered by mahdipoor last updated on 29/Dec/24 $${ab}+{ba}=\mathrm{11}\left({a}+{b}\right)=\mathrm{11}^{\mathrm{2}} ={n}^{\mathrm{2}}…

Question-215052

Question Number 215052 by Abdullahrussell last updated on 27/Dec/24 Answered by mr W last updated on 27/Dec/24 $${f}\left(\mathrm{1}\right)=\mathrm{1}\:\Rightarrow{f}\left({x}\right)=\left({x}−\mathrm{1}\right){g}\left({x}\right)+\mathrm{1} \\ $$$${f}\left(\mathrm{2}\right)=\left(\mathrm{2}−\mathrm{1}\right){g}\left(\mathrm{2}\right)+\mathrm{1}=\mathrm{4}\:\Rightarrow{g}\left(\mathrm{2}\right)=\mathrm{3}\:\Rightarrow{g}\left({x}\right)=\left({x}−\mathrm{2}\right){h}\left({x}\right)+\mathrm{3} \\ $$$$\Rightarrow{f}\left({x}\right)=\left({x}−\mathrm{1}\right)\left[\left({x}−\mathrm{2}\right){h}\left({x}\right)+\mathrm{3}\right]+\mathrm{1} \\ $$$${f}\left(\mathrm{3}\right)=\left(\mathrm{3}−\mathrm{1}\right)\left[\left(\mathrm{3}−\mathrm{2}\right){h}\left(\mathrm{3}\right)+\mathrm{3}\right]+\mathrm{1}=\mathrm{3}\:\Rightarrow{h}\left(\mathrm{3}\right)=−\mathrm{2}\:\Rightarrow{h}\left({x}\right)=\left({x}−\mathrm{3}\right){k}\left({x}\right)−\mathrm{2} \\…

x-2-2000x-1-0-Roots-a-and-b-x-2-2008x-1-0-Roots-c-and-d-Find-a-c-b-d-a-d-b-c-

Question Number 215072 by hardmath last updated on 27/Dec/24 $$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2000x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{Roots}:\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2008x}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{Roots}:\:\:\boldsymbol{\mathrm{c}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{d}} \\ $$$$\mathrm{Find}:\:\:\left(\mathrm{a}+\mathrm{c}\right)\left(\mathrm{b}+\mathrm{d}\right)\left(\mathrm{a}−\mathrm{d}\right)\left(\mathrm{b}−\mathrm{c}\right)\:=\:? \\ $$ Commented by TonyCWX08…

a-b-c-d-R-such-that-a-b-c-d-2-a-c-b-d-3-a-d-b-c-4-find-a-2-b-2-c-2-d-2-minimum-

Question Number 215005 by Abdullahrussell last updated on 25/Dec/24 $$\:{a},{b},{c},{d}\in{R}\:{such}\:{that}, \\ $$$$\:\left({a}+{b}\right)\left({c}+{d}\right)=\mathrm{2} \\ $$$$\:\left({a}+{c}\right)\left({b}+{d}\right)=\mathrm{3} \\ $$$$\:\left({a}+{d}\right)\left({b}+{c}\right)=\mathrm{4}\: \\ $$$$\:{find}:\:\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} \right)_{{minimum}.} \\ $$ Answered…