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Category: Algebra

let-p-x-x-4n-x-3n-x-2n-x-n-1-and-q-x-x-4-x-3-x-2-x-1-determine-the-integr-n-to-have-q-divide-p-

Question Number 50353 by prof Abdo imad last updated on 16/Dec/18 $${let}\:{p}\left({x}\right)={x}^{\mathrm{4}{n}} −{x}^{\mathrm{3}{n}} +{x}^{\mathrm{2}{n}} −{x}^{{n}} +\mathrm{1}\:{and} \\ $$$${q}\left({x}\right)={x}^{\mathrm{4}} −{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −{x}+\mathrm{1}\:\:{determine}\:{the}\:{integr}\:{n} \\ $$$${to}\:{have}\:{q}\:{divide}\:{p}. \\ $$…

solve-for-x-x-x-x-36-

Question Number 181415 by Socracious last updated on 24/Nov/22 $$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} } =\mathrm{36} \\ $$$$ \\ $$ Commented by Frix last updated on 25/Nov/22…

Question-115871

Question Number 115871 by bemath last updated on 29/Sep/20 Commented by bemath last updated on 29/Sep/20 $$\begin{pmatrix}{{m}\:\:\:{n}}\\{{n}\:\:\:{m}}\end{pmatrix}\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{\:\:\:\:\:\:\:\mathrm{1}}\\{\frac{\mathrm{3}{mn}}{\mathrm{2}{m}^{\mathrm{2}} +{n}^{\mathrm{2}} }}\end{pmatrix} \\ $$$$\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\frac{\mathrm{1}}{{m}^{\mathrm{2}} −{n}^{\mathrm{2}} }\:\begin{pmatrix}{{m}\:\:\:−{n}}\\{−{n}\:\:\:{m}}\end{pmatrix}\:\begin{pmatrix}{\:\:\:\:\:\:\:\mathrm{1}}\\{\frac{\mathrm{3}{mn}}{\mathrm{2}{m}^{\mathrm{2}} +{n}^{\mathrm{2}} }}\end{pmatrix}…

Question-50328

Question Number 50328 by peter frank last updated on 15/Dec/18 Answered by peter frank last updated on 16/Dec/18 $$\left.\mathrm{1}\right) \\ $$$${x}+\mathrm{2}{y}−\mathrm{3}{z}={a}…\left({i}\right) \\ $$$$\mathrm{2}{x}+\mathrm{6}{y}−\mathrm{11}{z}={b}…\left({ii}\right) \\ $$$${x}−\mathrm{2}{y}+\mathrm{7}{z}={c}….\left({iii}\right)…

What-are-all-ordered-pairs-of-real-number-x-y-for-which-5-y-x-x-y-1-and-x-y-x-y-5-

Question Number 115858 by bemath last updated on 29/Sep/20 $${What}\:{are}\:{all}\:{ordered}\:{pairs}\:{of}\:{real} \\ $$$${number}\:\left({x},{y}\right)\:{for}\:{which}\: \\ $$$$\mathrm{5}^{{y}−{x}} \:\left({x}+{y}\right)\:=\:\mathrm{1}\:{and}\:\left({x}+{y}\right)^{{x}−{y}} \:=\:\mathrm{5} \\ $$ Answered by floor(10²Eta[1]) last updated on 29/Sep/20…

What-are-all-real-values-of-p-for-which-the-inequality-3-lt-x-2-px-2-x-2-x-1-lt-2-is-satisfied-by-all-real-values-of-x-

Question Number 115857 by bemath last updated on 29/Sep/20 $${What}\:{are}\:{all}\:{real}\:{values}\:{of}\:{p}\:{for} \\ $$$${which}\:{the}\:{inequality}\: \\ $$$$−\mathrm{3}<\frac{{x}^{\mathrm{2}} +{px}−\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}<\mathrm{2}\:{is}\:{satisfied}\: \\ $$$${by}\:{all}\:{real}\:{values}\:{of}\:{x} \\ $$ Answered by bobhans last updated…

If-a-1-b-2-c-3-z-26-then-t-a-t-b-t-c-t-y-t-z-

Question Number 181375 by Tawa11 last updated on 24/Nov/22 $$\mathrm{If}\:\:\mathrm{a}\:=\:\mathrm{1},\:\mathrm{b}\:=\:\mathrm{2},\:\mathrm{c}\:=\:\mathrm{3},\:…\:\mathrm{z}\:\:=\:\:\mathrm{26} \\ $$$$\mathrm{then}\:\:\:\:\left(\mathrm{t}\:−\:\mathrm{a}\right)\left(\mathrm{t}\:−\:\mathrm{b}\right)\left(\mathrm{t}\:−\:\mathrm{c}\right)\:…\:\left(\mathrm{t}\:−\:\mathrm{y}\right)\left(\mathrm{t}\:−\:\mathrm{z}\right)\:=\:\:\:?? \\ $$ Commented by mr W last updated on 24/Nov/22 $$\:…\:\:{is}\:\left({t}−{d}\right)…\left({t}−{s}\right)\left({t}−{t}\right)\left({t}−{u}\right)…\left({t}−{x}\right) \\ $$…