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…
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…
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 Number 95767 by PengagumRahasiamu last updated on 27/May/20 Answered by prakash jain last updated on 27/May/20 $$\mathrm{characteric}\:\mathrm{equation} \\ $$$${x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}=\mathrm{0} \\ $$$${x}^{\mathrm{4}}…
Question Number 95766 by I want to learn more last updated on 27/May/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{2x}} \:\:−\:\:\mathrm{5x}^{\mathrm{2}} \:\:+\:\:\mathrm{4}\:\:\:=\:\:\:\mathrm{0} \\ $$ Commented by prakash jain last…
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…
Question Number 161295 by Ari last updated on 15/Dec/21 $${prove}\:{that}:{x}^{\mathrm{8}} +{x}^{\mathrm{6}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}>\mathrm{0},{x}\in{R} \\ $$ Commented by Ari last updated on 15/Dec/21 thanks Mr! Commented by…
Question Number 30218 by abdo imad last updated on 18/Feb/18 $${prove}\:{that}\:{D}\left({x}^{\mathrm{5}} −\mathrm{1},{x}^{\mathrm{2}} +{x}+\mathrm{1}\right)=\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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…
Question Number 161280 by HongKing last updated on 15/Dec/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{y}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{z}}\:=\:\mathrm{1} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{xyz} \\ $$ Answered by 1549442205PVT last updated on 16/Dec/21 $${From}\:{the}\:{hypothesis}\:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{y}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{z}}\:=\:\mathrm{1} \\…