Find the minimum value of P

Algebra Level 4

Give \( x, y\) are real numbers such that \( x<1, y>1\) and

\( \left\{\begin{matrix} \sqrt{x^2+1}+x=y-\sqrt{y^2-1} & \\ \left ( 1-x \right )\sqrt{x^2+1}=y\left ( \sqrt{y^2-1}+1 \right ) & \end{matrix}\right.\)

Find the minimum value of \[ P= \dfrac{1}{x^2}+y^2-1\]

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