Question

[kietdeptrai]

a) 4sqrt(2x + 1) - sqrt(8x + 4) + 1/2 * sqrt(32x + 16) = 12 b) sqrt(4x ^ 2 - 4x + 1) = 5 . c) (2sqrt(x) - 3)/(sqrt(x) - 1) = - 1/2

Answer 1

[HT.Phong (9A5)]

a) \(4\sqrt{2x+1}-\sqrt{8x+4}+\dfrac{1}{2}\sqrt{32x+16}=12\) (ĐK: \(x\ge-\dfrac{1}{2}\)) 

\(\Leftrightarrow4\sqrt{2x+1}-\sqrt{4\left(2x+1\right)}+\dfrac{1}{2}\cdot4\sqrt{2x+1}=12\)

\(\Leftrightarrow4\sqrt{2x+1}-2\sqrt{2x+1}+2\sqrt{2x+1}=12\)

\(\Leftrightarrow4\sqrt{2x+1}=12\)

\(\Leftrightarrow\sqrt{2x+1}=\dfrac{12}{4}\)

\(\Leftrightarrow2x+1=3^2\)

\(\Leftrightarrow2x=9-1\)

\(\Leftrightarrow2x=8\)

\(\Leftrightarrow x=\dfrac{8}{2}\)

\(\Leftrightarrow x=4\left(tm\right)\)

b) \(\sqrt{4x^2-4x+1}=5\)

\(\Leftrightarrow\sqrt{\left(2x-1\right)^2}=5\)

\(\Leftrightarrow\left|2x-1\right|=5\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5\left(x\ge\dfrac{1}{2}\right)\\2x-1=-5\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{2}\\x=-\dfrac{4}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)

c) \(\dfrac{2\sqrt{x}-3}{\sqrt{x}-1}=-\dfrac{1}{2}\)(ĐK: \(x\ge0;x\ne1\))

\(\Leftrightarrow-\left(\sqrt{x}-1\right)=2\left(2\sqrt{x}-3\right)\)

\(\Leftrightarrow-\sqrt{x}+1=4\sqrt{x}-6\)

\(\Leftrightarrow4\sqrt{x}+\sqrt{x}=1+6\)

\(\Leftrightarrow5\sqrt{x}=7\)

\(\Leftrightarrow\sqrt{x}=\dfrac{7}{5}\)

\(\Leftrightarrow x=\dfrac{49}{25}\left(tm\right)\)