[latex] egin{array}{ll} E=dfrac{m_0v^2}{sqrt{1-dfrac{v^2}{c^2}}} divdfrac{2}{1}&/cdot2\\ 2E=dfrac{m_0v^2}{sqrt{1-dfrac{v^2}{c^2}}} &frac{a}{b}=frac{c}{d}leftrightarrow ad=bc\\ m_0v^2=2Esqrt{1-dfrac{v^2}{c^2}} & a=a leftrightarrow a^2=a^2\\ &(p^qr^s)^k=p^{qk}r^{sk}\\ m_0^2v^4=4E^2(1-dfrac{v^2}{c^2})\\ m_0^2v^4=4E^2-dfrac{v^24E^2}{c^2}\\m_0^2v^4c^2=4E^2c^2-4E^2v^2 & /-(4E^2c^2-4E^2v^2)\\ end{array}[/latex] [latex]egin{array}{ll}\\m_0^2v^4c^2+4E^2v^2-4E^2c^2=0&u:=v^2\\ m_0^2c^2u^2+4E^2u-4E^2c^2=0&x_{1,2}=dfrac{-bpmsqrt{b^2-4ac}}{2a}\\ u_{1,2}=\ =dfrac{-4E^2pmsqrt{(4E^2)^2-4m_0^2c^2cdot-4E^2c^2}}{2m_0^2c^2}\ =dfrac{-4E^2pmsqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}\\ u_1=dfrac{-4E^2+sqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}\\ u_2=dfrac{-4E^2-sqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}\\ v=sqrt{dfrac{-4E^2+sqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}}\\ v=-sqrt{dfrac{-4E^2+sqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}}\\ v=sqrt{dfrac{-4E^2-sqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}}\\ v=-sqrt{dfrac{-4E^2-sqrt{16E^4+16m_0^2c^4E^2}}{2m_0^2c^2}}end{array} [/latex]
