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Question Number 11672 by @ANTARES_VY last updated on 29/Mar/17

8x^3 −6x+1=0  Solves...

$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{Solves}}... \\ $$

Commented by mrW1 last updated on 29/Mar/17

see general solution:

$${see}\:{general}\:{solution}: \\ $$

Commented by mrW1 last updated on 29/Mar/17

Commented by @ANTARES_VY last updated on 30/Mar/17

which  program told

$$\boldsymbol{\mathrm{which}}\:\:\boldsymbol{\mathrm{program}}\:\boldsymbol{\mathrm{told}} \\ $$

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/Mar/17

Δ=b^2 −3ac=0−3×8×(−6)=144⟩0  k=((−27a^2 d)/(2(√Δ^3 )))=−0.5⇒∣k∣≤1  x_1 =((2(√(Δ.))cos((1/3)cos^(−1) k)−b)/(3a))(/)=  x_1 =((−2×12cos(20)−0)/(3×8))=((24×0.9396)/(24))=−0.9396  x_2 =((−2×12cos(20−120))/(24))=0.1736  x_3 =((−2×12cos(20+120))/(24))=0.7660

$$\Delta={b}^{\mathrm{2}} −\mathrm{3}{ac}=\mathrm{0}−\mathrm{3}×\mathrm{8}×\left(−\mathrm{6}\right)=\mathrm{144}\rangle\mathrm{0} \\ $$$${k}=\frac{−\mathrm{27}{a}^{\mathrm{2}} {d}}{\mathrm{2}\sqrt{\Delta^{\mathrm{3}} }}=−\mathrm{0}.\mathrm{5}\Rightarrow\mid{k}\mid\leqslant\mathrm{1} \\ $$$${x}_{\mathrm{1}} =\frac{\mathrm{2}\sqrt{\Delta.}{cos}\left(\frac{\mathrm{1}}{\mathrm{3}}{cos}^{−\mathrm{1}} {k}\right)−{b}}{\mathrm{3}{a}}\frac{}{}= \\ $$$${x}_{\mathrm{1}} =\frac{−\mathrm{2}×\mathrm{12}{cos}\left(\mathrm{20}\right)−\mathrm{0}}{\mathrm{3}×\mathrm{8}}=\frac{\mathrm{24}×\mathrm{0}.\mathrm{9396}}{\mathrm{24}}=−\mathrm{0}.\mathrm{9396} \\ $$$${x}_{\mathrm{2}} =\frac{−\mathrm{2}×\mathrm{12}{cos}\left(\mathrm{20}−\mathrm{120}\right)}{\mathrm{24}}=\mathrm{0}.\mathrm{1736} \\ $$$${x}_{\mathrm{3}} =\frac{−\mathrm{2}×\mathrm{12}{cos}\left(\mathrm{20}+\mathrm{120}\right)}{\mathrm{24}}=\mathrm{0}.\mathrm{7660} \\ $$

Commented by @ANTARES_VY last updated on 30/Mar/17

8x^3 −6x+1=0     this  development  is  an  example?

$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0}\:\:\:\:\:\boldsymbol{\mathrm{this}}\:\:\boldsymbol{\mathrm{development}} \\ $$$$\boldsymbol{\mathrm{is}}\:\:\boldsymbol{\mathrm{an}}\:\:\boldsymbol{\mathrm{example}}? \\ $$

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