Question

Tìm x đễ mỗi biểu thức sau có nghĩa

a) √2019/x^2 b) √x^4+1 c) √x^2 +1/1-2x d) √x^2 -9 e) √4-x^2 f) √(3-5x)(x-6)

G) √x^3-8x-9 h)√16-x^2 i) √x^2-4x-5 k) √(x-2)(x-6) l) √-2/3x-1

Mn giúp mình với ạ!

Answer 1

Biểu thức có nghĩa khi :

a) \(\frac{2019}{x^2}\ge0\)( luôn đúng )

b) \(x^4+1\ge0\)( luôn đúng )

c) \(\frac{x^2+1}{1-2x}\ge0\Leftrightarrow1-2x>0\Leftrightarrow x< \frac{1}{2}\)

d) \(x^2-9\ge0\Leftrightarrow x^2\ge9\Leftrightarrow\left[{}\begin{matrix}x\ge3\\x\le-3\end{matrix}\right.\)

e) \(4-x^2\ge0\Leftrightarrow x^2\le4\Leftrightarrow-2\le x\le2\)

f) \(\left(3-5x\right)\left(x-6\right)\ge0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3-5x\ge0\\x-6\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}3-5x\le0\\x-6\le0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le\frac{3}{5}\\x\ge6\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge\frac{3}{5}\\x\le6\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}6\le x\le\frac{3}{5}\left(l\right)\\\frac{3}{5}\le x\le6\left(c\right)\end{matrix}\right.\)

g)h)i)k)l) tương tự, nhiều quá