Question

Hãy liệt kê các phần tử của tập hơp sau :
a) D=[x thuộc Z| 2x^2 - 5x + 3 = 0]
b) F=[x thuộc Z||x+2|<=1]
c) G=[x thuộc N| x<5]
d) H=[x thuộc R| x^2 + x + 3 = 0]

e)\(E=\left[x\in N|\left\{{}\begin{matrix}x+3< 4+2x\\5x-3< 4x-1\end{matrix}\right.\right]\)

 

Answer 1

a) \(2x^2-5x+3=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=1\end{matrix}\right.\) mà \(x\in Z\Rightarrow x=1\)

Vậy \(D=\left\{1\right\}\)

b) \(x\in Z\Rightarrow x+2\in Z\Rightarrow\left|x+2\right|\in Z\)

Mà \(\left|x+2\right|\le1\Rightarrow\left[{}\begin{matrix}\left|x+2\right|=0\\\left|x+2\right|=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x+2=0\\x+2=1\\x+2=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=-1\\x=-3\end{matrix}\right.\)

Vậy \(F=\left\{-3;-2;-1\right\}\)

c) \(G=\left\{x\in N|x< 5\right\}=\left\{0;1;2;3;4\right\}\)

d) \(x^2+x+3=\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{11}{4}=\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}>0\)

Vậy \(H=\varnothing\)

e) Ta có \(\left\{{}\begin{matrix}x+3< 4+2x\\5x-3< 4x-1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>-1\\x< 2\end{matrix}\right.\) mà \(x\in N\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Vậy \(E=\left\{0;1\right\}\)