Đáp án:
\[P = - 3\]
Giải thích các bước giải:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to \sqrt 2 } \frac{{3{x^2} - 2\sqrt 2 x - 2}}{{3x - 3\sqrt 2 }}\\
= \mathop {\lim }\limits_{x \to \sqrt 2 } \frac{{\left( {3{x^2} - 3\sqrt 2 x} \right) + \left( {\sqrt 2 x - 2} \right)}}{{3.\left( {x - \sqrt 2 } \right)}}\\
= \mathop {\lim }\limits_{x \to \sqrt 2 } \frac{{3x\left( {x - \sqrt 2 } \right) + \sqrt 2 \left( {x - \sqrt 2 } \right)}}{{2.\left( {x - \sqrt 2 } \right)}}\\
= \mathop {\lim }\limits_{x \to \sqrt 2 } \frac{{\left( {3x + \sqrt 2 } \right)\left( {x - \sqrt 2 } \right)}}{{2.\left( {x - \sqrt 2 } \right)}}\\
= \mathop {\lim }\limits_{x \to \sqrt 2 } \frac{{3x + \sqrt 2 }}{2}\\
= \frac{{3.\sqrt 2 + \sqrt 2 }}{2}\\
= \frac{{4\sqrt 2 }}{2}\\
= 2\sqrt 2 \\
\Rightarrow a = 2;\,\,\,\,b = 1\\
\Rightarrow P = {b^2} - 2a = - 3
\end{array}\)