Đáp án:
a) \(\left[ \begin{array}{l}
x = \sqrt 2 \\
x = - \sqrt 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
P\left( x \right) = 7{x^5} + \dfrac{1}{4}{x^2} - x - \dfrac{7}{2}\\
Q\left( x \right) = - 7{x^5} + \dfrac{1}{4}{x^2} + x + \dfrac{5}{2}\\
a)M\left( x \right) = P\left( x \right) + Q\left( x \right)\\
= 7{x^5} + \dfrac{1}{4}{x^2} - x - \dfrac{7}{2} - 7{x^5} + \dfrac{1}{4}{x^2} + x + \dfrac{5}{2}\\
= \dfrac{1}{2}{x^2} - 1\\
M\left( x \right) = 0\\
\to \dfrac{1}{2}{x^2} - 1 = 0\\
\to {x^2} = 2\\
\to \left[ \begin{array}{l}
x = \sqrt 2 \\
x = - \sqrt 2
\end{array} \right.\\
b)N\left( x \right) + Q\left( x \right) = P\left( x \right)\\
\to N\left( x \right) = P\left( x \right) - Q\left( x \right)\\
= 7{x^5} + \dfrac{1}{4}{x^2} - x - \dfrac{7}{2} + 7{x^5} - \dfrac{1}{4}{x^2} - x - \dfrac{5}{2}\\
= 14{x^5} - 2x - 6
\end{array}\)
