Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 111175 by 9696147350 last updated on 02/Sep/20

Answered by ajfour last updated on 02/Sep/20

$$\sqrt{x}=t$$$$t^4-\frac{3t}{2}+\frac{1}{2}=0,let$$$$(t^2+pt+q)(t^2-pt+\frac{1}{2q})=0$$$$\Rightarrow \frac{1}{2q}+q=p^2\mathrm{\&}\frac{1}{2q}-q=-\frac{3}{2p}$$$$\Rightarrow p^4-\frac{9}{4p^2}=2$$$$say{p}^2=z$$$$\Rightarrow z^3-2z-\frac{9}{4}=0$$$$z_0={(\frac{9}{8}+\sqrt{\frac{81}{64}-\frac{8}{27}})}^{1/3}-{(\frac{9}{8}-\sqrt{\frac{81}{64}-\frac{8}{27}})}^{1/3}$$$$sayp=\sqrt{z_0}$$$$q=\frac{z_0}{2}+\frac{3}{4\sqrt{z_0}},\frac{1}{2q}=\frac{z_0}{2}-\frac{3}{4\sqrt{z_0}}$$$$t=\frac{\sqrt{z_0}}{2}\pm \sqrt{\frac{z_0}{4}-\frac{z_0}{2}+\frac{3}{4\sqrt{z_0}}}$$$$\Rightarrow \sqrt{x}=t=\frac{\sqrt{z_0}}{2}\pm \sqrt{\frac{3}{4\sqrt{z_0}}-\frac{z_0}{4}}$$$$x=\frac{3}{4\sqrt{z_0}}\pm \frac{1}{2}\sqrt{3\sqrt{z_0}-z_0^2}$$$$....$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com