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Category: Algebra

Question-151241

Question Number 151241 by bagjagugum123 last updated on 19/Aug/21 Answered by hknkrc46 last updated on 19/Aug/21 $$\left(\mathrm{2}\right)\:\mid\mathrm{2}\boldsymbol{{x}}\:−\:\mathrm{3}\mid\:<\:\mid\boldsymbol{{x}}\:−\:\mathrm{1}\mid \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\left(\mathrm{2}\boldsymbol{{x}}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:<\:\left(\boldsymbol{{x}}\:−\:\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{12}\boldsymbol{{x}}\:+\:\mathrm{9}\:<\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{2}\boldsymbol{{x}}\:+\:\mathrm{1} \\…

Question-151224

Question Number 151224 by mathdanisur last updated on 19/Aug/21 Answered by Rasheed.Sindhi last updated on 19/Aug/21 $${Let}\:{there}'{re}\:{x}\:{boys}\:{and}\:{y}\:{girls} \\ $$$${minimum}\:{number}\:{of}\:{slices}\:{eaten} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4}{x}+\mathrm{2}{y} \\ $$$$\left(\mathrm{4}\:{slices}/{boy}\:\:\&\:\mathrm{2}\:{slices}/{girl}\right) \\ $$$$\mathrm{4}{x}+\mathrm{2}{y}>\mathrm{16}\:\:\left(\mathrm{2}\:{cakes},\:\mathrm{8}\:{slices}\:{per}\:{each}\:{cake}\right)…

if-a-1-a-2-a-n-gt-1-then-a-1-1-a-2-1-a-n-1-a-1-1-a-2-1-a-n-1-a-1-a-2-a-n-2-n-

Question Number 151212 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\:\:\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,…\mathrm{a}_{\boldsymbol{\mathrm{n}}} >\mathrm{1}\:\:\mathrm{then}: \\ $$$$\sqrt{\frac{\left(\mathrm{a}_{\mathrm{1}} -\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} -\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} -\mathrm{1}\right)}{\left(\mathrm{a}_{\mathrm{1}} +\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} +\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} +\mathrm{1}\right)}}\:\leqslant\:\frac{\mathrm{a}_{\mathrm{1}} \mathrm{a}_{\mathrm{2}} …\mathrm{a}_{\boldsymbol{\mathrm{n}}} }{\mathrm{2}^{\boldsymbol{\mathrm{n}}} }…

if-x-y-z-gt-0-x-y-z-1-and-1-6-then-y-z-x-3-yz-6-1-

Question Number 151215 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:;\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{1}\:\mathrm{and}\:\lambda\geqslant\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{then}: \\ $$$$\boldsymbol{\lambda}\:\Sigma\:\frac{\mathrm{y}\:+\:\mathrm{z}}{\mathrm{x}}\:+\:\mathrm{3}\:\Sigma\:\mathrm{yz}\:\geqslant\:\mathrm{6}\boldsymbol{\lambda}\:+\:\mathrm{1} \\ $$ Answered by dumitrel last updated on 19/Aug/21 $${p}=\mathrm{1} \\ $$$${p}^{\mathrm{2}} \geqslant\mathrm{3}{q}\Rightarrow{q}\leqslant\frac{\mathrm{1}}{\mathrm{3}}\leqslant\mathrm{2}\lambda…

determinant-2-3-x-1-2-2-3-x-x-

Question Number 151205 by EDWIN88 last updated on 19/Aug/21 $$\underbrace{ }\:\begin{array}{|c|c|}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} +\mathrm{1}\:=\left(\mathrm{2}\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} }\\{{x}\:=?\:}\\\hline\end{array} \\ $$ Answered by bramlexs22 last updated on 19/Aug/21 $$\:\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{x}} }\:+\:\mathrm{1}\:=\:\frac{\mathrm{2}^{\mathrm{x}} }{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\frac{\mathrm{x}}{\mathrm{2}}}…

Find-the-coefficient-of-x-9-from-expression-1-x-1-2x-2-1-3x-3-1-4x-4-1-5x-5-1-10x-10-

Question Number 151211 by EDWIN88 last updated on 19/Aug/21 $$\:{Find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{9}} \: \\ $$$${from}\:{expression}\: \\ $$$$\:\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{3}} \right)\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{4}} \right)\left(\mathrm{1}+\mathrm{5}{x}^{\mathrm{5}} \right)…\left(\mathrm{1}+\mathrm{10}{x}^{\mathrm{10}} \right) \\ $$ Answered by Olaf_Thorendsen…

Show-that-a-group-order-100-is-not-simple-

Question Number 85664 by Jidda28 last updated on 23/Mar/20 $$\boldsymbol{{S}\mathrm{how}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{group}}\:\boldsymbol{\mathrm{order}}\:\mathrm{100}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{not}}\:\boldsymbol{\mathrm{simple}} \\ $$ Commented by mind is power last updated on 24/Mar/20 $$\mathrm{100}=\mathrm{2}^{\mathrm{2}} .\mathrm{5}^{\mathrm{2}} \\ $$$${let}\:{see}\:{sylow}\:{Theorem}…