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Author: Tinku Tara

x-2-x-3y-11-y-2-y-3x-29-x-y-

Question Number 214499 by hardmath last updated on 10/Dec/24 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{x}\:\:+\:\:\mathrm{3y}\right)\:\:=\:\:\mathrm{11}}\\{\mathrm{y}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{y}\:\:+\:\:\mathrm{3x}\right)\:\:=\:\:\mathrm{29}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:? \\ $$ Commented by Frix last updated on 10/Dec/24 $$\mathrm{4}\:\mathrm{solutions} \\ $$$${x}+{y}={t} \\…

Question-214479

Question Number 214479 by Frangg last updated on 09/Dec/24 Answered by mehdee7396 last updated on 10/Dec/24 $$\frac{\mathrm{5}{x}−\mathrm{6}}{\mathrm{3}{x}}=\frac{\mathrm{26}}{\mathrm{18}}=\frac{\mathrm{13}}{\mathrm{9}} \\ $$$$\mathrm{45}{x}−\mathrm{54}=\mathrm{39}{x} \\ $$$$\mathrm{6}{x}=\mathrm{54}\Rightarrow{x}=\mathrm{9} \\ $$$$ \\ $$$$…

If-x-a-2-bc-y-b-2-ac-z-c-2-ab-Find-ax-by-cz-x-y-z-

Question Number 214456 by hardmath last updated on 09/Dec/24 $$\mathrm{If}\:\:\:\frac{\mathrm{x}}{\mathrm{a}^{\mathrm{2}} −\:\mathrm{bc}}\:=\:\frac{\mathrm{y}}{\mathrm{b}^{\mathrm{2}} −\:\mathrm{ac}}\:=\:\frac{\mathrm{z}}{\mathrm{c}^{\mathrm{2}} −\:\mathrm{ab}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{ax}\:+\:\mathrm{by}\:+\:\mathrm{cz}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}}\:=\:? \\ $$ Commented by Ghisom last updated on 09/Dec/24 $${a}+{b}+{c}…

If-x-2y-3z-2-x-2-y-2-z-2-14-find-x-y-z-

Question Number 214457 by hardmath last updated on 09/Dec/24 $$\mathrm{If}\:\:\:\frac{\left(\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{3z}\right)^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} }\:=\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\frac{\mathrm{x}\:+\:\mathrm{y}}{\mathrm{z}}\:=\:? \\ $$ Commented by Ghisom last updated on 09/Dec/24 $$\mathrm{1} \\…

lim-n-1-2-4-1-5-7-1-3n-1-3n-1-

Question Number 214485 by depressiveshrek last updated on 09/Dec/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{7}}+…+\frac{\mathrm{1}}{\left(\mathrm{3}{n}−\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{1}\right)}\right) \\ $$ Answered by mr W last updated on 10/Dec/24 $$\psi\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)=−\gamma+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}−\frac{\mathrm{1}}{\mathrm{3}}}\right) \\…

a-b-c-R-S-9a-b-c-16b-a-c-49c-a-b-min-S-

Question Number 214454 by hardmath last updated on 09/Dec/24 $$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{R}^{+} \\ $$$$\mathrm{S}\:\:=\:\:\frac{\mathrm{9a}}{\mathrm{b}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{16b}}{\mathrm{a}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{49c}}{\mathrm{a}\:+\:\mathrm{b}} \\ $$$$\boldsymbol{\mathrm{min}}\left(\mathrm{S}\right)\:=\:? \\ $$ Commented by Ghisom last updated on 09/Dec/24 $${S}>\mathrm{24} \\…