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y = A x 3 + B x 2 + C x + D {\displaystyle y=Ax^{3}+Bx^{2}+Cx+D\,}
m = 3 A x 2 + 2 B x + C {\displaystyle m=3Ax^{2}+2Bx+C\,}
( x 1 , y 1 ) , m 1 ; ( x 2 , y 2 ) , m 2 {\displaystyle (x_{1},y_{1}),m_{1};(x_{2},y_{2}),m_{2}\,}
x 1 , x 2 ≠ 0 ; x 1 ≠ x 2 {\displaystyle x_{1},x_{2}\neq 0;x1\neq x2\,}
( m 1 = 3 A x 1 2 + 2 B x 1 + C ) − ( m 2 = 3 A x 2 2 + 2 B x 2 + C ) {\displaystyle {\begin{aligned}(m_{1}&=3Ax_{1}^{2}+2Bx_{1}+C)\\-(m_{2}&=3Ax_{2}^{2}+2Bx_{2}+C)\\\end{aligned}}}
m 1 − m 2 = 3 A ( x 1 2 − x 2 2 ) + 2 B ( x 1 − x 2 ) {\displaystyle m_{1}-m_{2}=3A(x_{1}^{2}-x_{2}^{2})+2B(x_{1}-x_{2})\,}
2 B ( x 1 − x 2 ) = m 1 − m 2 − 3 A ( x 1 2 − x 2 2 ) {\displaystyle 2B(x_{1}-x_{2})=m_{1}-m_{2}-3A(x_{1}^{2}-x_{2}^{2})}
B = m 1 − m 2 − 3 A ( x 1 2 − x 2 2 ) 2 x 1 − 2 x 2 {\displaystyle B={\frac {m_{1}-m_{2}-3A(x_{1}^{2}-x_{2}^{2})}{2x_{1}-2x_{2}}}}
m 1 = 3 A x 1 2 + 2 B x 1 + C {\displaystyle m_{1}=3Ax_{1}^{2}+2Bx_{1}+C\,}
m 1 = 3 A x 1 2 + 2 [ m 1 − m 2 − 3 A ( x 1 2 − x 2 2 ) 2 x 1 − 2 x 2 ] x 1 + C {\displaystyle m_{1}=3Ax_{1}^{2}+2\left[{\frac {m_{1}-m_{2}-3A(x_{1}^{2}-x_{2}^{2})}{2x_{1}-2x_{2}}}\right]x_{1}+C\,}
C = m 1 − 3 A x 1 2 − [ m 1 − m 2 − 3 A ( x 1 2 − x 2 2 ) x 1 − x 2 ] x 1 {\displaystyle C=m_{1}-3Ax_{1}^{2}-\left[{\frac {m_{1}-m_{2}-3A(x_{1}^{2}-x_{2}^{2})}{x_{1}-x_{2}}}\right]x_{1}\,}
C = m 1 − m 1 − m 2 x 1 − x 2 − 3 A x 1 [ x 1 − ( x 1 + x 2 ) ] {\displaystyle C=m_{1}-{\frac {m_{1}-m_{2}}{x_{1}-x_{2}}}-3Ax_{1}\left[x_{1}-(x_{1}+x_{2})\right]\,}
![{\displaystyle m_{1}=3Ax_{1}^{2}+2\left[{\frac {m_{1}-m_{2}-3A(x_{1}^{2}-x_{2}^{2})}{2x_{1}-2x_{2}}}\right]x_{1}+C\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f90f4cf08312bd2453011497f860874a2159cb16)
![{\displaystyle C=m_{1}-3Ax_{1}^{2}-\left[{\frac {m_{1}-m_{2}-3A(x_{1}^{2}-x_{2}^{2})}{x_{1}-x_{2}}}\right]x_{1}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e531579481514c490e70d8b6b01d146a591dce0c)
![{\displaystyle C=m_{1}-{\frac {m_{1}-m_{2}}{x_{1}-x_{2}}}-3Ax_{1}\left[x_{1}-(x_{1}+x_{2})\right]\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d12885309896dbabeebb989eb702d4e0e535a9)
