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Category: Algebra

2-2-8-A-B-Find-A-B-

Question Number 215439 by hardmath last updated on 06/Jan/25 $$\left(\:\mathrm{2}\:\:+\:\:\sqrt{\mathrm{2}}\:\right)^{\mathrm{8}} \:=\:\:\sqrt{\mathrm{A}}\:\:+\:\:\sqrt{\mathrm{B}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{A}−\mathrm{B}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 07/Jan/25 $${If}\:{z}\:{is}\:{a}\:{binomial}\:{surd}\:{and}\:{n}\:{is} \\ $$$${natural}\:…

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}}…