Category: Algebra

Question Number 191624 by Shrinava last updated on 27/Apr/23 Answered by ARUNG_Brandon_MBU last updated on 28/Apr/23 $${\int }_1^x\sqrt{\frac{t}{1+t^3}}dt$$$$=\int_{\mathrm{1}} ^{{x}} \frac{{t}^{\frac{\mathrm{1}}{\mathrm{2}}} }{\:\sqrt{\mathrm{1}+\left({t}^{\frac{\mathrm{3}}{\mathrm{2}}}…

Question Number 191615 by MATHEMATICSAM last updated on 27/Apr/23 $$a+b+c=0.\mathrm{Prove}\mathrm{that},$$$$\frac{a}{a^2-bc}+\frac{b}{b^2-ca}+\frac{c}{c^2-ab}=0.$$ Answered by som(math1967) last updated on 27/Apr/23 $$\:{a}+{b}+{c}=\mathrm{0}…

Question Number 191610 by mehdee42 last updated on 27/Apr/23 $$Q:ifx+\frac{1}{x}=2cos\left(\theta \right)proveit{x}^n+\frac{1}{x^n}=2cos\left(n\theta \right)$$ Answered by Frix last updated on 27/Apr/23 $$z+\frac{1}{z}=2c\Rightarrow z=c\pm \sqrt{c^2-1}\Rightarrow$$$${x}=\mathrm{cos}\:\theta\:\pm\mathrm{i}\:\mathrm{sin}\:\theta\:=\mathrm{e}^{\pm\mathrm{i}\theta}…

Question Number 191595 by MATHEMATICSAM last updated on 26/Apr/23 $$a=\frac{xy}{x+y},b=\frac{xz}{x+z}\mathrm{and}c=\frac{yz}{y+z}.$$$$\mathrm{Represent}x\mathrm{in}a,b,c\mathrm{form}.[x,y,z\ne 0]$$ Answered by mehdee42 last updated on 26/Apr/23 $$\frac{1}{a}=\frac{1}{x}+\frac{1}{y}\left(i\right),\frac{1}{b}=\frac{1}{x}+\frac{1}{z}\left(ii\right),\frac{1}{c}=\frac{1}{y}+\frac{1}{z}\left(iii\right)$$$$\left({i}\right),\left({ii}\right)\Rightarrow\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}=\frac{\mathrm{2}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}\overset{\left({iii}\right)} {\Rightarrow}\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}=\frac{\mathrm{2}}{{x}}+\frac{\mathrm{1}}{{c}}…

Question Number 60500 by prof Abdo imad last updated on 21/May/19 $$letA=\left(\begin{array}{c}11\\ -23\end{array}\right)$$$$1)find{A}^{-1}$$$$2)calculate{A}^n$$$$3)determine{e}^{A}and{e}^{-2A}.$$ Commented by maxmathsup…