2.6315x=1-(1+x)^(-4)

asked by guest
on Jan 12, 2025 at 9:05 pm



You asked:

Solve the equation \(2.6315 x = 1 - {\left( 1 + x \right)}^{-4}\) for the variable \(x\).

MathBot Answer:

The complex solutions are: \[\left\{0, - \frac{4763}{5263} - \frac{\sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}{2} - \frac{i \sqrt{\left|{- \frac{133848676000}{145780726447 \sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}} - 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}} + \frac{48104000}{83097507} + \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}\right|}}{2}, - \frac{4763}{5263} - \frac{\sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}{2} + \frac{i \sqrt{\left|{- \frac{133848676000}{145780726447 \sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}} - 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}} + \frac{48104000}{83097507} + \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}\right|}}{2}, - \frac{4763}{5263} + \frac{\sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}{2} + \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}} + \frac{48104000}{83097507} + \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{133848676000}{145780726447 \sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}}\right|}}{2}, - \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}} + \frac{48104000}{83097507} + \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{133848676000}{145780726447 \sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}}\right|}}{2} - \frac{4763}{5263} + \frac{\sqrt{- \frac{67156000}{249292521 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}} + \frac{24052000}{83097507} + 2 \sqrt[3]{- \frac{69208750000}{3936079614069} + \frac{10000 \sqrt{47387160547905}}{1312026538023}}}}{2}\right\} \setminus \left\{-1\right\}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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