Question

Tìm x để căn thức sau có nghĩa

A) \(\sqrt{x+4-2\sqrt{x+3}}\)

B)\(\dfrac{1}{\sqrt{2x-\sqrt{4x-1}}}\)

C) \(\dfrac{1}{\sqrt{2-x^2}}\)

D) \(\dfrac{2}{\sqrt{6-x-x^2}}\)

Answer 1

a/ đkxđ: \(x+3\ge0\Leftrightarrow x\ge-3\)

b/ \(\left\{{}\begin{matrix}4x-1\ge0\\x\ne\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{4}\\x\ne\dfrac{1}{2}\end{matrix}\right.\)

c/ \(2-x^2>0\Leftrightarrow x^2< 2\Leftrightarrow-\sqrt{2}< x< \sqrt{2}\)

d/ \(6-x-x^2>0\Leftrightarrow\left(x+3\right)\left(2-x\right)>0\Leftrightarrow\left(x+3\right)\left(x-2\right)< 0\Leftrightarrow-3< x< 2\)