Question

a, 4x-√3(3x-1)=3x-1
b, 3√2(x+1)=1-4x
c, 6x-3√4(2x-1)=2x+1

Answer 1

a) \(4x-\sqrt[]{3\left(3x-1\right)}=3x-1\)

\(\Leftrightarrow\sqrt[]{3\left(3x-1\right)}=x+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1\ge0\\3\left(3x-1\right)=\left(x+1\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\9x-3=x^2+2x+1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\left(a\right)\\x^2-7x+4=0\left(1\right)\end{matrix}\right.\)

Giải \(pt\left(1\right):\)

\(\Delta=49-16=33\Rightarrow\sqrt[]{\Delta}=\sqrt[]{33}\)

Phương trình (1) có 2 nghiệm phân biệt

\(\left[{}\begin{matrix}x=\dfrac{7+\sqrt[]{33}}{2}\\x=\dfrac{7-\sqrt[]{33}}{2}\end{matrix}\right.\) (thỏa \(\left(a\right)\))