914.06 = 50/(1+Y)^1 + 1050(1+Y)^2

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on Jan 09, 2025 at 10:22 am



You asked:

Solve the equation \(914.06 = \frac{50}{{\left( 1 + Y \right)}^{1}} + 1050 {\left( 1 + Y \right)}^{2}\) for the variable \(Y\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}Y &= -1 - \frac{\sqrt{6529} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{75} \approx -1.9592575\\Y &= -1 - \frac{\sqrt{19587} \sin{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} - \frac{6529 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{14} + \frac{\sqrt{13321135270561} i}{875000}}}\right)}}{7500} + \frac{\sqrt{6529} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} + i \left(- \frac{6529 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{14} + \frac{\sqrt{13321135270561} i}{875000}}}\right)}}{7500} + \frac{\sqrt{6529} \sin{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} + \frac{\sqrt{19587} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300}\right) \approx -0.94510901 + 2.0 \cdot 10^{-143} i\\Y &= -1 + \frac{\sqrt{19587} \sin{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} + \frac{\sqrt{6529} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} - \frac{6529 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{14} + \frac{\sqrt{13321135270561} i}{875000}}}\right)}}{7500} + i \left(- \frac{\sqrt{19587} \cos{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} + \frac{\sqrt{6529} \sin{\left(\frac{\arctan{\left(\frac{\sqrt{13321135270561}}{562500} \right)}}{3} \right)}}{300} - \frac{6529 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{9}{14} + \frac{\sqrt{13321135270561} i}{875000}}}\right)}}{7500}\right) \approx -0.095633513 -2.0 \cdot 10^{-142} i\end{aligned}\]

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

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