(120/(y^2 - 12*y + 72))^2 + y^2 = 400

asked by guest
on Jan 25, 2025 at 6:18 am



You asked:

Solve the equation \({\left( \frac{120}{{y}^{2} - 12 y + 72} \right)}^{2} + {y}^{2} = 400\) for the variable \(y\).

MathBot Answer:

The complex solutions are: \[\left\{2 \operatorname{CRootOf} {\left(x^{6} - 12 x^{5} - 28 x^{4} + 984 x^{3} - 6876 x^{2} + 21600 x - 32175, 0\right)}, 2 \operatorname{CRootOf} {\left(x^{6} - 12 x^{5} - 28 x^{4} + 984 x^{3} - 6876 x^{2} + 21600 x - 32175, 1\right)}, 2 \operatorname{CRootOf} {\left(x^{6} - 12 x^{5} - 28 x^{4} + 984 x^{3} - 6876 x^{2} + 21600 x - 32175, 2\right)}, 2 \operatorname{CRootOf} {\left(x^{6} - 12 x^{5} - 28 x^{4} + 984 x^{3} - 6876 x^{2} + 21600 x - 32175, 3\right)}, 2 \operatorname{CRootOf} {\left(x^{6} - 12 x^{5} - 28 x^{4} + 984 x^{3} - 6876 x^{2} + 21600 x - 32175, 4\right)}, 2 \operatorname{CRootOf} {\left(x^{6} - 12 x^{5} - 28 x^{4} + 984 x^{3} - 6876 x^{2} + 21600 x - 32175, 5\right)}\right\} \setminus \left\{6 - 6 i, 6 + 6 i\right\}\]

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

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