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Category: Algebra

33-9-25-9-2-19-2-8-

Question Number 125785 by Mathgreat last updated on 13/Dec/20 $$\oplus+\oplus+\oplus=\mathrm{33} \\ $$$$\blacktriangle+\blacktriangle+\mathrm{9}\blacktrinagledown=\mathrm{25} \\ $$$$\mathrm{9}\blacktrinagledown+\blacktriangle+\mathrm{2}\bigstar=\mathrm{19} \\ $$$$\mathrm{2}\oplus+\mathrm{8}\blacktrinagledown\:\centerdot\:\bigstar=\:? \\ $$$$\:\: \\ $$ Answered by Olaf last updated…

Question-191304

Question Number 191304 by Mingma last updated on 22/Apr/23 Answered by cortano12 last updated on 22/Apr/23 $$\:\mathrm{x}=\mathrm{t}^{\mathrm{2}} −\mathrm{2}\: \\ $$$$\:\left(\mathrm{t}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{3}} −\mathrm{3}\left(\mathrm{t}^{\mathrm{2}} −\mathrm{2}\right)−\mathrm{t}=\mathrm{0} \\ $$$$\:\left(\mathrm{t}−\mathrm{2}\right)\left(\mathrm{2t}+\mathrm{1}−\sqrt{\mathrm{5}}\right)\left(\mathrm{2t}+\mathrm{1}+\sqrt{\mathrm{5}}\right)\left(\frac{\mathrm{1}}{\mathrm{4}}\mathrm{t}^{\mathrm{3}}…

Question-191300

Question Number 191300 by Mingma last updated on 22/Apr/23 Answered by Tinku Tara last updated on 22/Apr/23 $$\left({a}^{\mathrm{2}} −\mathrm{3}\right)\left({a}^{\mathrm{2}} −\mathrm{2}\right)\left({a}^{\mathrm{2}} −\mathrm{1}\right)\left({a}^{\mathrm{2}} \right)\left({a}^{\mathrm{2}} +\mathrm{1}\right)\left({a}^{\mathrm{2}} +\mathrm{2}\right)\left({a}^{\mathrm{2}} +\mathrm{3}\right)=\mathrm{8}!…

Question-191301

Question Number 191301 by Mingma last updated on 22/Apr/23 Answered by a.lgnaoui last updated on 23/Apr/23 $$\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\:\Rightarrow\left(\mathrm{a}+\mathrm{b}+\mathrm{c}>\mathrm{0}\:\:\:\mathrm{et}\:\mathrm{abc}>\mathrm{0}\right) \\ $$$$\mathrm{poxons}\:\:\mathrm{x}=\mathrm{abc}\:\:\:\:\:\mathrm{y}=\mathrm{a}+\mathrm{b}+\mathrm{c}\:\:\:\mathrm{xy}=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{c}}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{c}}=\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{b}} \\ $$$$\:\:\left(\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{c}}\right)\left(\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{b}}\right)\:=\boldsymbol{\mathrm{y}}^{\mathrm{2}} −\left(\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{bc}} \\…

Question-191283

Question Number 191283 by Shrinava last updated on 22/Apr/23 Answered by amin96 last updated on 22/Apr/23 $$\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{problem}}\:\boldsymbol{\mathrm{new}}\:\boldsymbol{\mathrm{RMM}}\:\boldsymbol{\mathrm{problem}} \\ $$$$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{my}}\:\boldsymbol{\mathrm{instagram}}\:\boldsymbol{\mathrm{page}}\: \\ $$$$ \\ $$@mathematics.azerbaijan Terms of…

x-y-z-simple-numbers-y-lt-x-lt-z-y-x-z-68-y-x-x-z-z-y-1121-y-x-

Question Number 125743 by MathSh last updated on 13/Dec/20 $$\boldsymbol{{x}}\:;\:\boldsymbol{{y}}\:;\:\boldsymbol{{z}}\:\rightarrow\:\boldsymbol{{simple}}\:\boldsymbol{{numbers}}\:, \\ $$$$\boldsymbol{{y}}<\boldsymbol{{x}}<\boldsymbol{{z}}\:, \\ $$$$\boldsymbol{{y}}+\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{68}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:+\:\boldsymbol{{x}}\:\centerdot\:\boldsymbol{{z}}\:+\:\boldsymbol{{z}}\:\centerdot\:\boldsymbol{{y}}\:=\:\mathrm{1121}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:=\:? \\ $$ Commented by MJS_new last updated…

solving-u-v-w-with-u-v-w-C-finding-all-possible-solutions-I-tested-this-with-several-values-and-found-no-mistake-please-review-and-comment-I-hope-this-will-help-at-least-some-of-you-

Question Number 60175 by MJS last updated on 18/May/19 $$\mathrm{solving}\:{u}^{{v}} ={w}\:\mathrm{with}\:{u},\:{v},\:{w}\:\in\mathbb{C} \\ $$$$\mathrm{finding}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions} \\ $$$$\mathrm{I}\:\mathrm{tested}\:\mathrm{this}\:\mathrm{with}\:\mathrm{several}\:\mathrm{values}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{no}\:\mathrm{mistake}.\:\mathrm{please}\:\mathrm{review}\:\mathrm{and}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{this}\:\mathrm{will}\:\mathrm{help}\:\mathrm{at}\:\mathrm{least}\:\mathrm{some}\:\mathrm{of}\:\mathrm{you}. \\ $$ Commented by MJS last…

Prove-by-principle-of-mathematical-induction-sin-x-sin-2x-sin-3x-sin-nx-cos-1-2-x-cos-n-1-2-x-2-sin-1-2-x-

Question Number 60156 by Tawa1 last updated on 18/May/19 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right)\:+\:…\:+\:\mathrm{sin}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)} \\ $$ Commented by Smail last updated on 19/May/19 $${sinx}+{sin}\mathrm{2}{x}+…+{sin}\left({nx}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{sin}\left({kx}\right) \\…