Question

Dạng \(\sqrt{f\left(x\right)}=g\left(x\right)\)

1 , \(9x+\sqrt{3x-2}=10\)

2 , \(\sqrt{3x-4}=x-3\)

3 , \(\sqrt{x^2-2x+3}=2x-1\)

4 , \(\sqrt{2x^2+3x+7}=x+2\)

5 , \(\sqrt{3x^2-4x-4}=\sqrt{2x+5}\)

Answer 1

1/ \(\left\{{}\begin{matrix}10-9x\ge0\\3x-2=\left(10-9x\right)^2\end{matrix}\right.< =>\left\{{}\begin{matrix}x\le\frac{10}{9}\\3x-2=100-180x+81x^2\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x\le\frac{10}{9}\\\left[{}\begin{matrix}x=\frac{34}{27}\left(l\right)\\x=1\end{matrix}\right.\end{matrix}\right.\)=> x=1

Vậy ....

Answer 2

2.\(\left\{{}\begin{matrix}x\ge3\\3x-4=\left(x-3\right)^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\3x-4=x^2-6x+9\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x\ge3&x=\frac{9\pm\sqrt{29}}{2}&\end{matrix}\right.\)=> \(x=\frac{9+\sqrt{29}}{2}\)

Vậy ....