Question

(*) tìm x để căn thức sau có nghĩa:

\(a,\sqrt{2x-1}\\ b,\sqrt{\dfrac{3}{x+1}}\\ c,\sqrt{3x^2}\\ d,\sqrt{\dfrac{3}{x^2}}\\ e,\sqrt{-\dfrac{1}{x^2+2}}\\ f,\sqrt{\dfrac{2}{3}x-\dfrac{1}{5}}\)

Answer 1

\(a,\sqrt{2x-1}\)

\(\sqrt{2x-1}\) có nghĩa khi:

\(2x-1\ge0\\ \Leftrightarrow2x\ge1\\ \Leftrightarrow x\ge\dfrac{1}{2}\)

\(b,\sqrt{\dfrac{3}{x^{ }+1}}\)

\(\sqrt{\dfrac{3}{x+1}}\) có nghĩa khi:

\(x+1\ge0\\ \Leftrightarrow x\ge-1\)

\(c,\sqrt{3x^2}\)

\(\forall x\in Rvì3x^2\ge0\)

\(d,\sqrt{\dfrac{3}{x^2}}\\ \forall x\in Rvìx^2\ge0\)

\(e,\sqrt{\dfrac{-1}{x^2+2}}\)

Không có nghĩa \(\forall x\in R\)

\(f,\sqrt{\dfrac{2}{3}x-\dfrac{1}{5}}\)

\(\sqrt{\dfrac{2}{3}x-\dfrac{1}{5}}\) có nghĩa khi:

\(\dfrac{2}{3}x-\dfrac{1}{5}\ge0\\ \)

\(\Leftrightarrow\)\(\dfrac{2}{3}x\ge\dfrac{1}{5}\\ \)

\(x\ge\dfrac{1}{10}\)