Solve Lesson 53 Page 17 Math 10 SBT – Kite>


Let A be the solution set of polynomial P(x), B be the set of solutions of polynomial Q(x), C be the set of solutions of the fraction \(\frac{{P(x)}}{{Q(x) }}\). Compare the set A\B and the set C

Detailed explanation

\(A\backslash B = \left\{ {x \in \mathbb{R}\left| {P(x) = 0,Q(x) \ne 0} \right.} \right\}\)

A is the root set of the polynomial P(x), so \(A = \left\{ {x \in \mathbb{R}|P(x) = 0} \right\}\)

B is the solution set of the polynomial Q(x), so \(B = \left\{ {x \in \mathbb{R}|Q(x) = 0} \right\}\)

Consider the equation: \(\frac{{P(x)}}{{Q(x)}} = 0\left( * \right)\)

The specified condition is \(Q\left( x \right) \ne 0\), then \(

\Leftrightarrow P(x) = 0\)

Experiment set of

are x values ​​such that \(P(x) = 0\) and \(Q(x) \ne 0\)

\( \Rightarrow C = \left\{ {x \in \mathbb{R}\left| {P(x) = 0;Q(x) \ne 0} \right.} \right\} = A{\ rm{\backslash }}B\)So \(C = A{\rm{\backslash }}B\)

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