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Category: Algebra

1-1-1-2-8-

Question Number 196066 by sniper237 last updated on 17/Aug/23 $$\begin{pmatrix}{\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}^{−\mathrm{8}} =\:\:? \\ $$ Answered by witcher3 last updated on 17/Aug/23 $$\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}=\mathrm{A} \\ $$$$\mathrm{A}^{\mathrm{2}} =\begin{pmatrix}{\mathrm{2}\:\:\:\:\:−\mathrm{3}}\\{−\mathrm{3}\:\:\:\:\mathrm{3}}\end{pmatrix}=\mathrm{3A}−\mathrm{I}_{\mathrm{2}} \\…

We-can-transform-to-get-rid-of-the-1-3-a-1-3-b-1-3-c-1-3-a-1-3-b-1-3-3-c-a-b-3a-1-3-b-1-3-a-1-3-b-1-3-c-3a-1-3-b-1-3-c-1-3-c-a-b-27abc-c-a-b-3-Is-it-

Question Number 195998 by Frix last updated on 15/Aug/23 $$\mathrm{We}\:\mathrm{can}\:\mathrm{transform}\:\mathrm{to}\:\mathrm{get}\:\mathrm{rid}\:\mathrm{of}\:\mathrm{the}\:\sqrt[{\mathrm{3}}]{…} \\ $$$${a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} ={c}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\left({a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)^{\mathrm{3}} ={c} \\ $$$${a}+{b}+\mathrm{3}{a}^{\frac{\mathrm{1}}{\mathrm{3}}} {b}^{\frac{\mathrm{1}}{\mathrm{3}}} \left({a}^{\frac{\mathrm{1}}{\mathrm{3}}} +{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \right)={c}…

Question-196015

Question Number 196015 by Ahmed777hamouda last updated on 15/Aug/23 Commented by Ahmed777hamouda last updated on 15/Aug/23 $$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{{i}}_{\boldsymbol{{D}}{p}} ,{i}_{{Dn}} \\ $$ Terms of Service Privacy Policy…

if-f-x-f-x-a-f-x-a-find-f-x-

Question Number 195971 by mr W last updated on 14/Aug/23 $${if}\:{f}'\left({x}\right)=\frac{{f}\left({x}+{a}\right)−{f}\left({x}\right)}{{a}},\:{find}\:{f}\left({x}\right). \\ $$ Answered by jabarsing last updated on 14/Aug/23 $${hello}\:{mr}.{w}\:{dear} \\ $$$${f}\left({x}\right)={C}\:\:\:\:\left({conestant}\:{function}\right)=? \\ $$$${is}\:{true}?…

Question-195898

Question Number 195898 by Calculusboy last updated on 12/Aug/23 Answered by qaz last updated on 13/Aug/23 $${a}_{{n}+\mathrm{2}} {a}_{{n}+\mathrm{1}} −{a}_{{n}+\mathrm{1}} {a}_{{n}} =\mathrm{2}\:\:\:\:\Rightarrow{a}_{{n}+\mathrm{2}} {a}_{{n}+\mathrm{1}} =\mathrm{2}{n}+{a}_{\mathrm{1}} {a}_{\mathrm{2}} =\mathrm{2}\left({n}+\mathrm{1}\right)…

a-b-c-gt-0-amp-abc-1-prove-that-1-1-a-b-1-1-b-c-1-1-c-a-1-

Question Number 195820 by York12 last updated on 11/Aug/23 $${a},{b},{c}>\mathrm{0}\:\&{abc}=\mathrm{1},{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{a}+{b}}+\frac{\mathrm{1}}{\mathrm{1}+{b}+{c}}+\frac{\mathrm{1}}{\mathrm{1}+{c}+{a}}\leqslant\mathrm{1} \\ $$ Answered by CrispyXYZ last updated on 12/Aug/23 $$\mathrm{let}\:{a}={x}^{\mathrm{3}} ,\:{b}={y}^{\mathrm{3}} ,\:{c}={z}^{\mathrm{3}} ,\:\mathrm{then}\:{xyz}=\mathrm{1}.…