Question

Hãy liệt kê cấc phần tử của tập X={x∈Q | (x²-x-6)(x²-5)=0}

A. x={-\(\sqrt{5}\); -2; \(\sqrt{5}\); 3}

B. x={\(\sqrt{5}\); 3}

C. x={-2; 3}

D. x={-\(\sqrt{5}\); \(\sqrt{5}\)}

Answer 1

\(\left(x^2-x-6\right)\left(x^2-5\right)=0\)

\(\Rightarrow\left(x-3\right)\left(x+2\right)\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=\sqrt{5}\\x=-\sqrt{5}\end{matrix}\right.\)

Mà \(x\in Q\)

\(\Rightarrow x=\left\{-2;3\right\}\)

Answer 2

Pt\(\Leftrightarrow\)\(\left[{}\begin{matrix}x^2-x-6=0\\x^2-5=0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}3\\-2\\-\sqrt{5}\\\sqrt{5}\end{matrix}\right.\)

   Đáp án A