Question Number 184270 by mathlove last updated on 04/Jan/23 $$\sqrt[{\mathrm{6}}]{−\mathrm{64}}\centerdot\sqrt[{\mathrm{7}}]{−\mathrm{128}}=? \\ $$ Answered by HeferH last updated on 04/Jan/23 $$\sqrt[{\mathrm{6}}]{−\mathrm{1}\centerdot\mathrm{2}^{\mathrm{6}} }\:\centerdot\:\sqrt[{\mathrm{7}}]{−\mathrm{1}\centerdot\mathrm{2}^{\mathrm{7}} }\:=\:\mathrm{2}{i}\centerdot\mathrm{2}{i}\:=\:\mathrm{4}{i}^{\mathrm{2}} =−\mathrm{4} \\ $$$$\:{mistake}:\:\sqrt[{\mathrm{6}}]{−\mathrm{1}}\:,\:\sqrt[{\mathrm{7}}]{−\mathrm{1}}\:\neq\:{i}…
Question Number 184258 by universe last updated on 04/Jan/23 $$\:\:\:\mathrm{2yz}−\mathrm{4z}+\mathrm{2x}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\mathrm{2xz}−\mathrm{2z}+\mathrm{2y}−\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\mathrm{2xy}−\mathrm{4x}−\mathrm{2y}+\mathrm{2z}+\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:? \\ $$ Answered by SEKRET last updated on 04/Jan/23…
Question Number 118712 by 1549442205PVT last updated on 19/Oct/20 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{inequalities}: \\ $$$$\left.\mathrm{1}\right)\left(\frac{\mathrm{n}+\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{n}} >\mathrm{n}!\:\mathrm{for}\:\forall\mathrm{n}\in\mathrm{N}^{\ast} ,\mathrm{n}>\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\mid\mathrm{sinnx}\mid\leqslant\mathrm{n}\mid\mathrm{sinx}\mid\:\mathrm{for}\:\forall\mathrm{n}\in\mathrm{N}^{\ast} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 184251 by Shrinava last updated on 04/Jan/23 $$\mathrm{If}\:\:\:\mathrm{x}\:\sqrt{\mathrm{y}}\:=\:\mathrm{2904} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{y}=? \\ $$ Answered by SEKRET last updated on 04/Jan/23 $$\:\:\:\boldsymbol{\mathrm{x}}\centerdot\sqrt{\boldsymbol{\mathrm{y}}}\:=\:\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} \\ $$$$\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{2}}…
Question Number 184242 by Shrinava last updated on 04/Jan/23 Answered by SEKRET last updated on 04/Jan/23 $$\:\boldsymbol{\mathrm{metod}}\:\boldsymbol{\mathrm{Kramer}} \\ $$$$\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}\right)\:=\:\:\begin{vmatrix}{\mathrm{4}}&{−\mathrm{5}}&{\:\:\mathrm{2}}\\{\mathrm{3}}&{−\mathrm{2}}&{\:\:\:\mathrm{7}}\\{\mathrm{3}}&{\mathrm{10}}&{−\mathrm{2}}\end{vmatrix}=\:−\mathrm{327} \\ $$$$\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}_{\mathrm{1}} \right)=\:\begin{vmatrix}{\mathrm{9}}&{−\mathrm{5}}&{\mathrm{2}}\\{\mathrm{8}}&{−\mathrm{2}}&{\mathrm{7}}\\{\mathrm{17}}&{\mathrm{10}}&{−\mathrm{2}}\end{vmatrix}=\:−\mathrm{1041} \\ $$$$\:\:\boldsymbol{\mathrm{det}}\left(\boldsymbol{\mathrm{A}}_{\mathrm{2}} \right)=\:\begin{vmatrix}{\mathrm{4}}&{\mathrm{9}}&{\mathrm{2}}\\{\mathrm{3}}&{\mathrm{8}}&{\mathrm{7}}\\{\mathrm{3}}&{\mathrm{17}}&{−\mathrm{2}}\end{vmatrix}=\:−\mathrm{243}…
Question Number 53144 by mr W last updated on 18/Jan/19 $${Find}\:{all}\:{integers}\:{x}\:{and}\:{y}\:{such}\:{that} \\ $$$$\frac{{xy}}{{x}+{y}}\:{is}\:{also}\:{integer}. \\ $$ Commented by mr W last updated on 19/Jan/19 $$\boldsymbol{{x}}=\left(\boldsymbol{{i}}+\mathrm{1}\right)\boldsymbol{{j}} \\…
Question Number 118651 by Sherjon last updated on 18/Oct/20 Commented by Sherjon last updated on 18/Oct/20 $${x}_{\mathrm{1}} +{x}_{\mathrm{2}} +…=?\:\:\:{Why} \\ $$ Commented by bramlexs22 last…
Question Number 53108 by Tawa1 last updated on 17/Jan/19 $$\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:+\:\mathrm{2}}\:\:−\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:−\:\mathrm{3}}\:\:\:>\:\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by kaivan.ahmadi last updated on 17/Jan/19 $$\mathrm{t}^{\mathrm{3}} =\mathrm{x}−\mathrm{3}\Rightarrow\mathrm{t}^{\mathrm{3}} +\mathrm{5}=\mathrm{x}+\mathrm{2}\Rightarrow \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{t}^{\mathrm{3}} +\mathrm{5}}\rangle\mathrm{t}+\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\mathrm{power}\:\mathrm{3}…
Question Number 118636 by Algoritm last updated on 18/Oct/20 Commented by TANMAY PANACEA last updated on 18/Oct/20 $${what}\:{is}\:{the}\:{question} \\ $$ Commented by Algoritm last updated…
Question Number 118634 by ajfour last updated on 18/Oct/20 $${Prove}\:{that}\:{the}\:{equation}\:{of}\:{the}\:{circle} \\ $$$${passing}\:{through}\:{the}\:{points}\:{of} \\ $$$${intersection}\:{of}\:{these}\:{two}\:{curves}: \\ $$$$\:\:{y}=\mathrm{1}+\frac{{c}}{{x}}\:;\:\:{y}={x}^{\mathrm{2}} \:\:\:\:\:\left({c}\:<\:\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\:\right)\: \\ $$$${is}\:\:\:\left({x}−\frac{{c}}{\mathrm{2}}\right)^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{1}+\frac{{c}^{\mathrm{2}} }{\mathrm{4}}\:\:. \\ $$ Commented…