(-60) + 28 / (x^1) + 28/ (x^2) + 28/ (x^3) + 28/ (x^4) = 0
asked by guest
on Jan 07, 2025 at 3:00 am
You asked:
Solve the equation
− 60 + 28 x 1 + 28 x 2 + 28 x 3 + 28 x 4 = 0 -60 + \frac{28}{{x}^{1}} + \frac{28}{{x}^{2}} + \frac{28}{{x}^{3}} + \frac{28}{{x}^{4}} = 0 − 60 + x 1 28 + x 2 28 + x 3 28 + x 4 28 = 0 for the variable
x x x .
MathBot Answer:
The complex solutions are: { 7 60 + − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 2 + ∣ − 2 − 7987 291600 + 7 26331753 486000 3 + 329 450 + 679 2025 − 7987 291600 + 7 26331753 486000 3 + 15883 13500 − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 ∣ 2 , − − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 2 + 7 60 − i ∣ − 15883 13500 − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 − 2 − 7987 291600 + 7 26331753 486000 3 + 329 450 + 679 2025 − 7987 291600 + 7 26331753 486000 3 ∣ 2 , − − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 2 + 7 60 + i ∣ − 15883 13500 − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 − 2 − 7987 291600 + 7 26331753 486000 3 + 329 450 + 679 2025 − 7987 291600 + 7 26331753 486000 3 ∣ 2 , − ∣ − 2 − 7987 291600 + 7 26331753 486000 3 + 329 450 + 679 2025 − 7987 291600 + 7 26331753 486000 3 + 15883 13500 − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 ∣ 2 + 7 60 + − 679 2025 − 7987 291600 + 7 26331753 486000 3 + 329 900 + 2 − 7987 291600 + 7 26331753 486000 3 2 } ∖ { 0 } \left\{\frac{7}{60} + \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2} + \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}}\right|}}{2}, - \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2} + \frac{7}{60} - \frac{i \sqrt{\left|{- \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}} - 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}\right|}}{2}, - \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2} + \frac{7}{60} + \frac{i \sqrt{\left|{- \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}} - 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}\right|}}{2}, - \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}} + \frac{329}{450} + \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{15883}{13500 \sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}}\right|}}{2} + \frac{7}{60} + \frac{\sqrt{- \frac{679}{2025 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}} + \frac{329}{900} + 2 \sqrt[3]{- \frac{7987}{291600} + \frac{7 \sqrt{26331753}}{486000}}}}{2}\right\} \setminus \left\{0\right\} ⎩ ⎨ ⎧ 60 7 + 2 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 + 2 − 2 3 − 291600 7987 + 486000 7 26331753 + 450 329 + 2025 3 − 291600 7987 + 486000 7 26331753 679 + 13500 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 15883 , − 2 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 + 60 7 − 2 i − 13500 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 15883 − 2 3 − 291600 7987 + 486000 7 26331753 + 450 329 + 2025 3 − 291600 7987 + 486000 7 26331753 679 , − 2 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 + 60 7 + 2 i − 13500 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 15883 − 2 3 − 291600 7987 + 486000 7 26331753 + 450 329 + 2025 3 − 291600 7987 + 486000 7 26331753 679 , − 2 − 2 3 − 291600 7987 + 486000 7 26331753 + 450 329 + 2025 3 − 291600 7987 + 486000 7 26331753 679 + 13500 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 15883 + 60 7 + 2 − 2025 3 − 291600 7987 + 486000 7 26331753 679 + 900 329 + 2 3 − 291600 7987 + 486000 7 26331753 ⎭ ⎬ ⎫ ∖ { 0 }
i i i is the imaginary unit , defined as i 2 = − 1 i^2 = -1 i 2 = − 1 .