Question

Answer 1

b) ĐKXĐ: \(x\ge\dfrac{2}{3}\)

\(\Leftrightarrow4\sqrt{3x-2}+2\sqrt{2x-1}=2\sqrt{3x-2}+4\sqrt{2x-1}\\ \Leftrightarrow2\sqrt{3x-2}=2\sqrt{2x-1}\\ \Leftrightarrow\sqrt{3x-2}=\sqrt{2x-1}\\ \Leftrightarrow3x-2=2x-1\\ \Leftrightarrow x=1\)

c) ĐKXĐ:\(x\ge\dfrac{2}{3}\)

\(\Leftrightarrow5\sqrt{3x-2}+3\sqrt{2x-1}=4\sqrt{3x-2}+4\sqrt{2x-1}\\ \Leftrightarrow\sqrt{3x-2}=\sqrt{2x-1}\\ \Leftrightarrow3x-2=2x-1\\ \Rightarrow x=1\)

Answer 2

\(b,ĐK:x\ge\dfrac{2}{3}\\ PT\Leftrightarrow4\sqrt{3x-2}+2\sqrt{2x-1}=2\sqrt{3x-2}+4\sqrt{2x-1}\\ \Leftrightarrow2\sqrt{3x-2}=2\sqrt{2x-1}\\ \Leftrightarrow3x-2=2x-1\\ \Leftrightarrow x=1\left(tm\right)\\ c,ĐK:x\ge\dfrac{2}{3}\\ PT\Leftrightarrow5\sqrt{3x-2}+3\sqrt{2x-1}=4\sqrt{3x-2}+4\sqrt{2x-1}\\ \Leftrightarrow\sqrt{3x-2}=\sqrt{2x-1}\\ \Leftrightarrow3x-2=2x-1\Leftrightarrow x=1\left(tm\right)\)

Answer 3

b) ĐKXĐ: \(x\ge\dfrac{2}{3}\)

\(pt\Leftrightarrow2\sqrt{12x-8}+2\sqrt{2x-1}=\sqrt{12x-8}+4\sqrt{2x-1}\)

\(\Leftrightarrow\sqrt{12x-8}-2\sqrt{2x-1}=0\)

\(\Leftrightarrow12x-8+8x-4=2.2\sqrt{\left(12x-8\right)\left(2x-1\right)}\)

\(\Leftrightarrow5x-3=\sqrt{24x^2-28x+8}\)

\(\Leftrightarrow25x^2-30x+9=24x^2-28x+8\)

\(\Leftrightarrow x^2-2x+1=0\Leftrightarrow\left(x-1\right)^2=0\Leftrightarrow x=1\left(tm\right)\)

c) ĐKXĐ: \(x\ge\dfrac{2}{3}\)

\(pt\Leftrightarrow5\sqrt{3x-2}+3\sqrt{2x-1}=4\sqrt{3x-2}+4\sqrt{2x-1}\)

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

\(\Leftrightarrow3x-2=2x-1\Leftrightarrow x=1\left(tm\right)\)