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Category: Algebra

somebody-has-posted-following-question-and-then-deleted-it-again-u-n-1-4u-n-9-u-n-2-u-0-5-find-u-n-or-something-like-this-

Question Number 214566 by mr W last updated on 12/Dec/24 $${somebody}\:{has}\:{posted}\:{following} \\ $$$${question}\:{and}\:{then}\:{deleted}\:{it}\:{again}. \\ $$$$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{\mathrm{4}{u}_{{n}} −\mathrm{9}}{{u}_{{n}} −\mathrm{2}}}\\{{u}_{\mathrm{0}} =\mathrm{5}}\end{cases} \\ $$$${find}\:{u}_{{n}} =?\:\left({or}\:{something}\:{like}\:{this}\right) \\ $$ Answered…

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} \\…

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} \\…

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} \\…

If-x-y-z-xyz-Find-x-1-y-2-1-z-2-y-1-x-2-1-z-2-z-1-x-2-1-y-2-2xyz-

Question Number 214455 by hardmath last updated on 09/Dec/24 $$\mathrm{If}\:\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{xyz} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{z}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{2xyz}} \\ $$ Commented by Ghisom…

a-b-c-d-e-f-Q-1-2-2-1-3-2-a-2-b-2-c-2-d-2-e-2-f-find-a-b-c-d-e-f-

Question Number 214443 by hardmath last updated on 08/Dec/24 $$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:\in\:\mathrm{Q} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{2}}}\:=\:\mathrm{2}^{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{c}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{d}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{e}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{f}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:=\:? \\ $$ Answered by ajfour last…