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

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



You asked:

Solve the equation 2.6315x=1−(1+x)−42.6315 x = 1 - {\left( 1 + x \right)}^{-4} for the variable xx.

MathBot Answer:

The complex solutions are: {0,−47635263−−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+1000047387160547905131202653802332−i∣−133848676000145780726447−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+100004738716054790513120265380233−2−692087500003936079614069+100004738716054790513120265380233+4810400083097507+67156000249292521−692087500003936079614069+100004738716054790513120265380233∣2,−47635263−−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+1000047387160547905131202653802332+i∣−133848676000145780726447−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+100004738716054790513120265380233−2−692087500003936079614069+100004738716054790513120265380233+4810400083097507+67156000249292521−692087500003936079614069+100004738716054790513120265380233∣2,−47635263+−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+1000047387160547905131202653802332+∣−2−692087500003936079614069+100004738716054790513120265380233+4810400083097507+67156000249292521−692087500003936079614069+100004738716054790513120265380233+133848676000145780726447−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+100004738716054790513120265380233∣2,−∣−2−692087500003936079614069+100004738716054790513120265380233+4810400083097507+67156000249292521−692087500003936079614069+100004738716054790513120265380233+133848676000145780726447−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+100004738716054790513120265380233∣2−47635263+−67156000249292521−692087500003936079614069+100004738716054790513120265380233+2405200083097507+2−692087500003936079614069+1000047387160547905131202653802332}∖{−1}\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\}

ii is the imaginary unit, defined as i2=−1i^2 = -1.

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