82
FORMULES.
et l’équation
donnera :
![{\displaystyle \operatorname {Log} .(x-4)+\operatorname {Log} .(x+4)+\operatorname {Log} .(x-3)+\operatorname {Log} .(x+3)-}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6504fff203a5a79abd108ea685529638acd2b56e)
![{\displaystyle 2\operatorname {Log} .x-\operatorname {Log} .(x-5)-\operatorname {Log} .(x+5)=2\mathrm {M\left[\mathrm {T} +{\tfrac {1}{3}}\mathrm {T} ^{3}+{\tfrac {1}{5}}\mathrm {T} ^{5}+{\text{ etc.}}\right]} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6a8316dc09e11fa46bc1d0046b1783d77fb3d7c9)
Cette formule a été trouvée par M. Haros, employé aux bureaux du cadastre[1].
42. 4.me formule. Si on suppose
dans les équations
K (n.o 14), on aura les suivantes ;
![{\displaystyle x^{4}+10x^{3}+25x^{2}-36=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d81beb586e49df5db4470e133a51ab06c807900)
et
![{\displaystyle x^{4}+10x^{3}+25x^{2}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0e11ff1360395e20ba7d5df548147d5cefe615a)
ou
![{\displaystyle (x+6)(x+3)(x+2)(x-1)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e75316e9cb698b579ff98f23965778d9a611c611)
et
![{\displaystyle x^{2}(x+5)^{2}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e64c0da709783315d684aa4920a870118665dca3)
faisant ensuite :
![{\displaystyle u=x^{4}+10x^{3}+25x^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c309a73d1d57d36cd26ad663da81fde466aa39f3)
et
![{\displaystyle t=x^{4}+10x^{3}+25x^{-}36}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a14f62407b09888363727f775aef840ac14f0378)
il viendra :
![{\displaystyle u-t=36}](https://wikimedia.org/api/rest_v1/media/math/render/svg/67c22ac63859fabd47311478d343e6dbd5c723da)
![{\displaystyle u+t=2x^{4}+20x^{3}+50x^{2}-36}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ba57d3a25695ec5649b326853ec3ae0561c06fb3)
![{\displaystyle {\frac {u-t}{u+t}}={\frac {18}{x^{4}+10x^{3}+25x^{2}-18}}=\mathrm {T} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6da03f6a05c34c29c4288c2d1dfe507089a9f76)
et l’équation
donnera :
![{\displaystyle \operatorname {Log} .(x+6)+\operatorname {Log} .(x+3)+\operatorname {Log} .(x+2)+\operatorname {Log} .(x-1)-}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cbc45f5cb7b2a85abd3971be1b8126d6f9e01e7)
![{\displaystyle 2\operatorname {Log} .(x+5)-2\operatorname {Log} .x=2\mathrm {M\left[\mathrm {T} +{\frac {1}{3}}\mathrm {T} ^{3}+{\frac {1}{5}}\mathrm {T} ^{5}+{\text{ etc.}}\right]} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1167bc21b664ce0e42b3aaf54cc6a4acf9bcc325)
- ↑ Voyez le Complément d’Algèbre de M. Lacroix.