Category: Algebra

Question Number 180381 by Linton last updated on 11/Nov/22 $$\sqrt{\frac{8^{12}+4^{13}}{8^6+4^{14}}}$$ Answered by floor(10²Eta[1]) last updated on 11/Nov/22 $$\sqrt{\frac{\mathrm{2}^{\mathrm{36}} +\mathrm{2}^{\mathrm{26}}…

Question Number 180351 by MikeH last updated on 10/Nov/22 $$\mathrm{solve}\mathrm{the}\mathrm{differential}\mathrm{equation}{y}^{″}+2y^{\prime }+y=0$$$$\mathrm{using}\mathrm{power}\mathrm{series}\mathrm{method}\mathrm{that}\mathrm{is},\mathrm{assume}$$$$y=\underset{n=0}{\sum ^{\mathrm{\infty }}}{c}_n{x}^n\mathrm{is}\mathrm{a}\mathrm{solution}$$ Terms of Service Privacy Policy…

Question Number 114809 by bemath last updated on 21/Sep/20 $$\{\begin{array}{l}1-\frac{12}{y+3x}=\frac{2}{\sqrt{x}}\\ 1+\frac{12}{y+3x}=\frac{6}{\sqrt{y}}\end{array}$$ Commented by bemath last updated on 21/Sep/20 $$set\sqrt{x}=u\wedge \sqrt{y}=v$$$$\iff \frac{12}{y+3x}=\frac{12}{y+3x}\Rightarrow 1-\frac{2}{u}=\frac{6}{v}-1$$$$\Rightarrow\:\mathrm{1}\:=\:\frac{\mathrm{1}}{{u}}+\frac{\mathrm{3}}{{v}};\:\mathrm{3}{u}+{v}\:=\:{uv} \…

Question Number 114806 by Algoritm last updated on 21/Sep/20 Answered by MJS_new last updated on 21/Sep/20 $$a-8=\frac{\sqrt{24}}{\sqrt{a}}$$$$\mathrm{let}a=t^2\wedge t>0$$$$t^2-8=\frac{2\sqrt{6}}{t}$$$${t}^{\mathrm{3}}…

Question Number 114796 by Algoritm last updated on 21/Sep/20 Answered by MJS_new last updated on 21/Sep/20 $$y=\frac{x}{2+y}=\frac{x}{2+\frac{x}{2+y}}=\frac{x}{2+\frac{x}{2+\frac{x}{2+y}}}=\dots$$$$\Rightarrow y=-1+\sqrt{x+1}$$$$\mathrm{but}\mathrm{the}\mathrm{last}\mathrm{term}1+\sqrt{x+1}=2+y$$$$\Rightarrow \mathrm{solution}\mathrm{is}-1+\sqrt{x+1}$$…