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Category: Algebra

similar-question-reposted-if-a-3-b-b-3-c-c-3-a-with-a-b-c-and-a-b-c-R-find-abc-2-

Question Number 161366 by mr W last updated on 17/Dec/21 $$\left[{similar}\:{question}\:{reposted}\right] \\ $$$${if}\:{a}+\frac{\mathrm{3}}{{b}}={b}+\frac{\mathrm{3}}{{c}}={c}+\frac{\mathrm{3}}{{a}}\:{with}\:{a}\neq{b}\neq{c} \\ $$$${and}\:{a},{b},{c}\:\in\:\mathbb{R}.\:{find}\:\left({abc}\right)^{\mathrm{2}} =? \\ $$ Answered by 1549442205PVT last updated on 18/Dec/21…

Prove-that-n-0-1-n-2n-1-0-1-0-1-dxdy-x-2-y-2-n-2-3-

Question Number 161353 by HongKing last updated on 16/Dec/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{2n}\:+\:\mathrm{1}}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{dxdy}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)^{\boldsymbol{\mathrm{n}}} }\:=\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$ Terms…

Can-We-expand-the-following-expression-1-x-1-2x-1-3x-1-nx-or-is-there-any-formula-for-this-

Question Number 30267 by Nayon.Sm last updated on 19/Feb/18 $${Can}\:{We}\:{expand}\:{the}\:{following} \\ $$$${expression}? \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}+\mathrm{3}{x}\right)……\left(\mathrm{1}+{nx}\right) \\ $$$${or}\:{is}\:{there}\:{any}\:{formula}\:{for}\:{this}? \\ $$ Commented by Penguin last updated on 19/Feb/18…

Find-the-semi-interquartile-range-of-of-the-following-numbers-15-10-9-15-15-8-10-11-8-12-11-14-9-and-15-

Question Number 95789 by Don08q last updated on 27/May/20 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{semi}−\mathrm{interquartile}\:\mathrm{range}\:\mathrm{of}\: \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{numbers}: \\ $$$$\:\mathrm{15},\:\mathrm{10},\:\mathrm{9},\:\mathrm{15},\:\mathrm{15},\:\mathrm{8},\:\mathrm{10},\:\mathrm{11},\:\mathrm{8},\:\mathrm{12},\:\mathrm{11},\:\mathrm{14}, \\ $$$$\:\mathrm{9}\:\mathrm{and}\:\mathrm{15} \\ $$ Commented by Don08q last updated on 27/May/20…

Question-95767

Question Number 95767 by PengagumRahasiamu last updated on 27/May/20 Answered by prakash jain last updated on 27/May/20 $$\mathrm{characteric}\:\mathrm{equation} \\ $$$${x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}=\mathrm{0} \\ $$$${x}^{\mathrm{4}}…

Sum-the-series-2-1-40-1-20-1-10-n-

Question Number 95765 by I want to learn more last updated on 27/May/20 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{40}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{20}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}}\:\:+\:\:…\:\:+\:\:\boldsymbol{\mathrm{n}}\right) \\ $$ Commented by prakash jain last updated on…

let-p-x-x-3-px-q-1-prove-that-p-have-double-roots-4p-3-27q-2-0-3-let-suppose-p-have-3-real-roots-differnts-prove-that-4p-3-27q-2-lt-0-

Question Number 30220 by abdo imad last updated on 18/Feb/18 $${let}\:{p}\left({x}\right)=\:{x}^{\mathrm{3}} \:{px}\:+{q} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{p}\:{have}\:{double}\:{roots}\Leftrightarrow\:\mathrm{4}{p}^{\mathrm{3}} \:+\mathrm{27}{q}^{\mathrm{2}} =\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{suppose}\:{p}\:{have}\:\mathrm{3}\:{real}\:{roots}\:{differnts}\:{prove}\:{that} \\ $$$$\mathrm{4}{p}^{\mathrm{3}} \:+\mathrm{27}{q}^{\mathrm{2}} \:<\mathrm{0}. \\ $$ Commented…