3o On prendra
![{\displaystyle m''<{\frac {{\sqrt {7}}+2}{3}},\quad m''>{\frac {{\sqrt {7}}+2}{3}}-1\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7242f43274895bf05e50c370002b96d78a79f1ea)
donc
d’où
![{\displaystyle q''=-1,\quad r'''=2\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab9735ed06b76d66b6398d99f858b7aa3a5ea729)
ensuite de quoi on aura
![{\displaystyle q'''=-1+2m''',\quad r^{\scriptscriptstyle {\text{IV}}}={\frac {7-q'''^{2}}{2}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/74698770a4b4cbc20a1f63d41d58ffdd96e00a6d)
donc, pour que
ne soit pas
il faudra prendre
ce qui donnera
![{\displaystyle q'''=1,\quad r^{\scriptscriptstyle {\text{IV}}}=3\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/816c36527269d6ef7272a14dc6b4c25deff921a2)
de là on aura la nouvelle transformée
![{\displaystyle 2y^{\scriptscriptstyle {\text{IV2}}}+2y^{\scriptscriptstyle {\text{IV}}}y'''-3y'''^{2},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0cc0160dd4b550acb2f0664fb029b890db90dba2)
qui aura aussi les conditions requises.
4o On fera
![{\displaystyle m'''<{\frac {{\sqrt {7}}+1}{2}},\quad m'''>{\frac {{\sqrt {7}}+1}{2}}-1\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30b85112d086186ce777620e03347bddee280dc9)
donc
et de là
![{\displaystyle q'''=1,\quad r^{\scriptscriptstyle {\text{IV}}}=3\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/816c36527269d6ef7272a14dc6b4c25deff921a2)
ensuite on aura
![{\displaystyle q^{\scriptscriptstyle {\text{IV}}}=1-3m^{\scriptscriptstyle {\text{IV}}},\quad r^{\scriptscriptstyle {\text{V}}}={\frac {7-q^{\scriptscriptstyle {\text{IV2}}}}{3}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c7aa785f6d02e263f3aa755bc4aea020d928917)
où l’on voit qu’on ne saurait prendre
en sorte que
ne devienne pas ![{\displaystyle >{\frac {r^{\scriptscriptstyle {\text{IV}}}}{2}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b329366a0ce9b888dbfd2f900eb965f8d5968593)
5o On fera
![{\displaystyle m^{\scriptscriptstyle {\text{IV}}}<{\frac {{\sqrt {7}}+1}{3}},\quad m^{\scriptscriptstyle {\text{IV}}}>{\frac {{\sqrt {7}}+1}{3}}-1,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fefcc3c8979b46a4d60c4c39b6881321e769bafd)
donc
et de là
![{\displaystyle q^{\scriptscriptstyle {\text{IV}}}=-2,\quad r^{\scriptscriptstyle {\text{V}}}=1\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d602c5133bcf7516fe55db20bcf6a98accf12435)
ensuite on aura
![{\displaystyle q^{\scriptscriptstyle {\text{V}}}=-2+m^{\scriptscriptstyle {\text{V}}},\quad r^{\scriptscriptstyle {\text{VI}}}={\frac {7-q^{\scriptscriptstyle {\text{V2}}}}{1}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c0c68020245639ed8fb22933a78c010ac609968)