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Algebra Level 4

Consider a Euclidean space \(\mathbb R^{n}\) and the 3 equations \[\begin{array} &y_{1}=x_{1}^{3}+x_{2}-1, &y_{2}=x_{1}^{3}, &y_{3}=x_{1}+x_{2}+2.\end{array}\] Now, a transformation \(T:\mathbb R^{2}\mapsto \mathbb R^{3}\) is defined by : \[T\left ( x_{1},x_{2} \right )=\left (x_{1}^{3}+x_{2}-1,x_{1}+x_{2}, x_{1}+x_{2}+2 \right ).\] Find \(T\left (2,8 \right )\).

Submit your answer as \(y_{1}+y_{2}-y_{3}\).

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