Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 124619 by arkanmath7@gmail.com last updated on 04/Dec/20

$$findtheinverseofy=x^4-2\mathit{x}+1$$

Commented by MJS_new last updated on 04/Dec/20

$$x^4-2x-(y+1)=0$$$$x=?$$$$\mathrm{can}\mathrm{only}\mathrm{be}\mathrm{solved}\mathrm{using}\mathrm{the}\mathrm{complete}\mathrm{path}$$$$\mathrm{of}\mathrm{Ferrari}.\mathrm{I}\mathrm{found}\mathrm{no}\mathrm{easier}\mathrm{path};\mathrm{if}\mathrm{you}\mathrm{have}$$$$\mathrm{a}\mathrm{solution},\mathrm{please}\mathrm{share}\mathrm{it}$$

Commented by arkanmath7@gmail.com last updated on 04/Dec/20

$$ActuallyIlookfortheanswer$$

Answered by ajfour last updated on 04/Dec/20

$$y=(x^2-mx+p)(x^2+mx+q)$$$$p+q=m^2$$$$m(p-q)=-2$$$$pq=1$$$$letp+q=\lambda$$$$\lambda ({\lambda }^2-4)=4$$$${\lambda }^3-4\lambda -4=0$$$$D=4-\frac{64}{27}>0$$$$so\lambda from{Cardano}^{\prime }s.$$$$\lambda \approx 2.38298$$$$forpandq$$$$z^2-\lambda z+1=0$$$$p,q=z=\frac{\lambda }{2}\pm \sqrt{\frac{{\lambda }^2}{4}-1}$$$$=0.54369,1.83929$$$$letp>q\Rightarrow p=1.83929,q=0.54369$$$$m=-\frac{2}{p-q}=-1.54368632$$$$x^2+mx+q=0$$$$x^2-1.54368632x+0.54369=0$$$$x=0.54369,1$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com