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Category: Algebra

What-it-s-5-55-555-5555-55555-

Question Number 164425 by Zaynal last updated on 17/Jan/22 $$\mathrm{What}\:\mathrm{it}'\mathrm{s}\:?? \\ $$$$\mathrm{5}×\mathrm{55}×\mathrm{555}×\mathrm{5555}×\mathrm{55555}………….\infty= \\ $$ Answered by alephzero last updated on 17/Jan/22 $$\mathrm{Let}\:{a}_{{n}} \:=\:\underset{{n}-\mathrm{times}} {\underbrace{\mathrm{5555}…\mathrm{5555}}} \\…

Question-164417

Question Number 164417 by HongKing last updated on 16/Jan/22 Answered by Rasheed.Sindhi last updated on 17/Jan/22 $${y}=\mathrm{4}{x}−\mathrm{3} \\ $$$$\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{6}{y}+\mathrm{9}}\:+\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}{y}+\mathrm{2}}\: \\ $$$$=\sqrt{{x}^{\mathrm{2}}…

if-a-b-c-lt-0-and-a-b-c-3-prove-that-1-b-a-1-b-2-1-c-b-1-c-2-1-a-c-1-a-2-8-

Question Number 164416 by HongKing last updated on 16/Jan/22 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}<\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\left(\mathrm{1}\:+\:\frac{\mathrm{b}}{\mathrm{a}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}^{\mathrm{2}} }} \centerdot\:\left(\mathrm{1}\:+\:\frac{\mathrm{c}}{\mathrm{b}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{c}}^{\mathrm{2}} }} \centerdot\:\left(\mathrm{1}\:+\:\frac{\mathrm{a}}{\mathrm{c}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} }} \geqslant\:\mathrm{8} \\ $$ Terms of Service Privacy Policy…

let-a-b-c-gt-0-a-b-c-3-prove-that-a-2-b-2-bc-c-2-b-2-c-2-ac-a-2-c-2-b-2-ba-a-2-6-2abc-5-3-a-2-b-2-c-2-7-Z-A-

Question Number 164405 by Zaynal last updated on 16/Jan/22 $$\boldsymbol{{let}}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:>\:\mathrm{0}\:;\:\boldsymbol{{a}}\:+\:\boldsymbol{{b}}\:+\:\boldsymbol{{c}}\:=\:\mathrm{3} \\ $$$$\boldsymbol{{prove}}\:\boldsymbol{{that}};\:\frac{\boldsymbol{{a}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} \:+\:\boldsymbol{{bc}}\:+\:\boldsymbol{{c}}^{\mathrm{2}} }\:\:+\:\:\frac{\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{c}}^{\mathrm{2}} \:+\:\boldsymbol{{ac}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} \:}\:\:+\:\:\frac{\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} \:+\boldsymbol{{ba}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} }\:\:\mathrm{6}\:\:\geqslant\:\:\mathrm{2}\boldsymbol{{abc}}\:\:+\:\:\frac{\mathrm{5}}{\mathrm{3}}\:\:\left(\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} \:+\:\boldsymbol{{c}}^{\mathrm{2}} \:\right)\:\:\geqslant\:\:\mathrm{7} \\…

Question-98859

Question Number 98859 by peter frank last updated on 16/Jun/20 Commented by mr W last updated on 16/Jun/20 $${p}\left({x}\right)={q}\left({x}\right)\left({x}−\mathrm{1}\right) \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$\mathrm{1}+{c}−\mathrm{2}{c}+\mathrm{4}=\mathrm{0} \\ $$$$\Rightarrow{c}=\mathrm{5}…

let-f-x-be-a-dolvnomial-of-degree-4-such-that-f-1-1-f-2-2-f-3-3-f-4-4-then-f-6-

Question Number 98842 by  M±th+et+s last updated on 16/Jun/20 $${let}\:{f}\left({x}\right)\:{be}\:{a}\:{dolvnomial}\:{of}\:{degree}\:\mathrm{4}\: \\ $$$${such}\:{that}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:,\:{f}\left(\mathrm{2}\right)=\mathrm{2}\:,{f}\left(\mathrm{3}\right)=\mathrm{3},{f}\left(\mathrm{4}\right)=\mathrm{4} \\ $$$${then}\:{f}\left(\mathrm{6}\right)=? \\ $$ Commented by mr W last updated on 16/Jun/20 $${see}\:{also}\:{Q}\mathrm{98268}…