Question Number 85871 by M±th+et£s last updated on 25/Mar/20 Commented by Rio Michael last updated on 25/Mar/20 $$\mathrm{all}\:\mathrm{integers} \\ $$ Commented by mr W last…
Question Number 85864 by john santu last updated on 26/Mar/20 $${simplify}\:{the}\:{expression} \\ $$$$\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{8}\sqrt{\mathrm{3}}−\mathrm{10}}}\:−\:\sqrt{\mathrm{7}−\sqrt{\mathrm{3}}}\:\:{in} \\ $$$${the}\:{form}\:\sqrt{\sqrt{{a}}+{b}}\:? \\ $$ Answered by jagoll last updated on 26/Mar/20 $$\mathrm{by}\:\mathrm{trick}\:!\:…
Question Number 151393 by Tawa11 last updated on 20/Aug/21 Answered by mr W last updated on 20/Aug/21 $$\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +…\right)^{\mathrm{3}} \left(\mathrm{1}+{x}^{\mathrm{5}} +{x}^{\mathrm{10}} +{x}^{\mathrm{15}} +…\right) \\ $$$$=\left(\mathrm{1}+{x}^{\mathrm{5}}…
Question Number 85854 by jagoll last updated on 25/Mar/20 $$\mathrm{If}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{4xyz}\:−\mathrm{1}\: \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\: \\ $$ Commented by mr W…
Question Number 151391 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b}\in\mathbb{R}\:\:\mathrm{and} \\ $$$$\left(\mathrm{a}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{b}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{9}=\mathrm{6}\left(\mathrm{a}+\mathrm{b}\right) \\ $$$$\mathrm{find}\:\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =? \\ $$ Answered by dumitrel last updated…
Question Number 151383 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y}>\mathrm{0}\:\:\mathrm{peove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}}{\mathrm{3}}\:\centerdot\:\frac{\mathrm{2}}{\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\centerdot\:\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\:\geqslant\:\mathrm{xy} \\ $$ Commented by mathdanisur last updated on 20/Aug/21 $$\mathrm{Thank}\:\mathrm{You}\:\mathrm{Dear}\:\boldsymbol{\mathrm{S}}\mathrm{er},\:\geqslant\sqrt[{\mathrm{3}}]{\mathrm{xy}}\:\mathrm{for}\:\mathrm{solution}\:\mathrm{please} \\…
Question Number 20308 by Tinkutara last updated on 25/Aug/17 $$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:{k},\:\left({x}\:+\:{y}\:+\:{z}\right)^{\mathrm{2}} \:+ \\ $$$${k}\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{resolved}\:\mathrm{into} \\ $$$$\mathrm{linear}\:\mathrm{rational}\:\mathrm{factors}? \\ $$ Answered by Tinkutara last updated…
Question Number 20307 by Tinkutara last updated on 25/Aug/17 $$\mathrm{Show}\:\mathrm{that}\:{a}\left({b}\:−\:{c}\right){x}^{\mathrm{2}} \:+\:{b}\left({c}\:−\:{a}\right){xy}\:+ \\ $$$${c}\left({a}\:−\:{b}\right){y}^{\mathrm{2}} \:\mathrm{will}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}\:\mathrm{if}\:{a}, \\ $$$${b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{H}.\mathrm{P}. \\ $$ Answered by ajfour last updated on 25/Aug/17…
Question Number 151371 by mathdanisur last updated on 20/Aug/21 $$\mathrm{a};\mathrm{b}\in\mathbb{N} \\ $$$$\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{2}} \centerdot\left(\mathrm{a}-\mathrm{b}\right)=\mathrm{128} \\ $$$$\mathrm{ab}=? \\ $$ Answered by nimnim last updated on 20/Aug/21 $$\mathrm{a};\mathrm{b}\in\mathrm{N}…
Question Number 20298 by mondodotto@gmail.com last updated on 25/Aug/17 Answered by Tinkutara last updated on 25/Aug/17 $$\mathrm{45}\:=\:\mathrm{36}\:+\:\mathrm{12}\:+\:\mathrm{18}\:−\:{n}\left(\mathrm{medals}\:\mathrm{in}\:\mathrm{two}\right. \\ $$$$\left.\mathrm{categories}\right)\:+\:\mathrm{4} \\ $$$${n}\left(\mathrm{medals}\:\mathrm{in}\:\mathrm{two}\:\mathrm{categories}\right)\:=\:\mathrm{25} \\ $$$${n}\left(\mathrm{exactly}\:\mathrm{two}\:\mathrm{categories}\right)\:=\:\mathrm{25}−\mathrm{3}×\mathrm{4} \\ $$$$=\:\mathrm{13}…