Question Number 151198 by liberty last updated on 19/Aug/21 $$\mathrm{If}\:{a},\mathrm{b}\in\mathrm{R}\:\mathrm{satisfy}\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} −\mathrm{6}{a}^{\mathrm{2}} {b}^{\mathrm{2}} =\mathrm{9}\:{and} \\ $$$${ab}\left({a}−{b}\right)\left({a}+{b}\right)=−\mathrm{11}\:\mathrm{then}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =? \\ $$ Answered by EDWIN88 last updated…
Question Number 151189 by mathdanisur last updated on 18/Aug/21 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship} \\ $$$$\mathrm{holds}:\:\left(\boldsymbol{\varphi}-\mathrm{golden}\:\mathrm{ratio}\right) \\ $$$$\mathrm{sinA}\:+\:\frac{\mathrm{sinB}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{sinC}}{\boldsymbol{\varphi}}\:<\:\frac{\mathrm{1}}{\boldsymbol{\varphi}}\:+\:\frac{\mathrm{1}+\sqrt{\boldsymbol{\varphi}}+\boldsymbol{\varphi}}{\mathrm{2}\boldsymbol{\varphi}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20118 by Tinkutara last updated on 22/Aug/17 $$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{equations}\:{x}^{\mathrm{2}} \:−\:\mathrm{6}{x}\:+\:{a}\:=\:\mathrm{0} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} \:−\:{cx}\:+\:\mathrm{6}\:=\:\mathrm{0}\:\mathrm{have}\:\mathrm{one}\:\mathrm{root}\:\mathrm{in} \\ $$$$\mathrm{common}.\:\mathrm{The}\:\mathrm{other}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{and}\:\mathrm{second}\:\mathrm{equations}\:\mathrm{are}\:\mathrm{integers}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{ratio}\:\mathrm{4}\::\:\mathrm{3}.\:\mathrm{Then},\:\mathrm{find}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{root}. \\ $$ Answered…
Question Number 85655 by Power last updated on 23/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20116 by Tinkutara last updated on 22/Aug/17 $$\mathrm{If}\:{a}\:\mathrm{and}\:{b}\:\left(\neq\:\mathrm{0}\right)\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:\left({x}\:\in\:{R}\right). \\ $$ Answered by ajfour last updated on 22/Aug/17…
Question Number 151191 by mathdanisur last updated on 18/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20115 by Tinkutara last updated on 22/Aug/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{1}\:−\:{a}^{\mathrm{2}} \right){x}^{\mathrm{2}} \:+\:\mathrm{2}{ax}\:−\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{has}\:\mathrm{roots} \\ $$$$\mathrm{belonging}\:\mathrm{to}\:\left(\mathrm{0},\:\mathrm{1}\right)\:\mathrm{is} \\ $$ Answered by ajfour last updated on 22/Aug/17…
Question Number 151181 by mathdanisur last updated on 18/Aug/21 $$\mathrm{if}\:\:\mid\boldsymbol{\mathrm{x}}\mid<\mathrm{1} \\ $$$$\mathrm{find}\:\:\mathrm{x}−\mathrm{4x}^{\mathrm{2}} +\mathrm{9x}^{\mathrm{3}} −\mathrm{16x}^{\mathrm{4}} +… \\ $$ Answered by Olaf_Thorendsen last updated on 18/Aug/21 $$\mathrm{S}\left({x}\right)\:=\:−\underset{{n}=\mathrm{1}}…
Question Number 151179 by mathdanisur last updated on 18/Aug/21 $$\mathrm{if}\:\:\mid\boldsymbol{\mathrm{x}}\mid<\mathrm{1} \\ $$$$\mathrm{find}\:\:\mathrm{x}+\mathrm{2x}^{\mathrm{2}} +\mathrm{3x}^{\mathrm{3}} +… \\ $$ Answered by Olaf_Thorendsen last updated on 18/Aug/21 $$\mathrm{S}\left({x}\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 151174 by mathdanisur last updated on 18/Aug/21 $$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}\centerdot…}}}}}}\:\:=\:\mathrm{3}\: \\ $$$$\mathrm{find}\:\:{a}=? \\ $$ Answered by mr W last updated on 18/Aug/21 $$\sqrt[{\mathrm{3}}]{{a}+\sqrt{\mathrm{3}×\mathrm{3}}}=\mathrm{3} \\ $$$${a}+\mathrm{3}=\mathrm{27}…