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Category: Algebra

Question-166058

Question Number 166058 by cortano1 last updated on 12/Feb/22 Answered by som(math1967) last updated on 12/Feb/22 $$\bigtriangleup{ABC}\sim\bigtriangleup{ALB}\sim\bigtriangleup{CLB} \\ $$$${let}\:\measuredangle{BAC}=\measuredangle{DCL}=\alpha \\ $$$${AL}×{AC}={a}^{\mathrm{2}} \\ $$$${AL}=\frac{{a}^{\mathrm{2}} }{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}}…

Find-x-in-R-x-2-x-6-How-to-solve-

Question Number 166053 by neinhaltsieger last updated on 12/Feb/22 $$\:\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{x}}\:\:\boldsymbol{\mathrm{in}}\:\:\mathbb{R}\overset{\:} {:} \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{x}}^{\sqrt{\mathrm{2}}} \:\:+\:\:\boldsymbol{\mathrm{x}}\:\:=\:\:\mathrm{6}\:\:\:\:\:\left(\boldsymbol{\mathrm{How}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{solve}}?\right) \\ $$ Commented by MJS_new last updated on 12/Feb/22…

16-64-16-64-16-64-16-1-3-2-1-2-1-2-1-2-1-3-

Question Number 100492 by bobhans last updated on 27/Jun/20 $$\sqrt[{\mathrm{3}\:\:\:}]{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−…}}}}−\sqrt[{\mathrm{3}\:\:}]{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−\frac{\mathrm{1}}{−\mathrm{2}−…}}}} \\ $$ Commented by Dwaipayan Shikari last updated on 27/Jun/20 $$\mathrm{p}=\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{\mathrm{16}−\frac{\mathrm{64}}{…..}}} \\ $$$$\mathrm{p}=\mathrm{16}−\frac{\mathrm{64}}{\mathrm{p}}\Rightarrow\mathrm{p}^{\mathrm{2}} −\mathrm{16p}+\mathrm{64}=\mathrm{0}\Rightarrow\mathrm{p}=\mathrm{8} \\…

x-2-y-2-z-2-70-x-3-y-3-z-3-64-x-4-y-4-z-4-2002-x-y-y-z-z-x-Use-Newton-Identities-or-otherwise-

Question Number 166009 by Rasheed.Sindhi last updated on 11/Feb/22 $$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{70}}\\{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{64}}\\{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =\mathrm{2002}}\\{\left({x}+{y}\right)\left({y}+{z}\right)\left({z}+{x}\right)=?}\end{cases}\: \\ $$$$\left({Use}\:\boldsymbol{{Newton}}-\boldsymbol{{Identities}}\right. \\ $$$$\left.{or}\:{otherwise}\right) \\ $$…

f-x-5x-2-a-f-1-x-x-b-5-faind-a-b-

Question Number 165949 by mathlove last updated on 10/Feb/22 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{2}}{{a}}\:\:\wedge{f}^{−\mathrm{1}} \left({x}\right)=\frac{{x}+{b}}{\mathrm{5}} \\ $$$${faind}\:\:\:{a}×{b}=? \\ $$ Answered by qaz last updated on 10/Feb/22 $$\left(\frac{\mathrm{5x}−\mathrm{2}}{\mathrm{a}}\right)'\centerdot\left(\frac{\mathrm{x}+\mathrm{b}}{\mathrm{5}}\right)'=\frac{\mathrm{1}}{\mathrm{a}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{a}=\mathrm{1}…