Question

Giải các phương trình sau:

a) √x-2 - 3√x^2 -4 = 0 b) 2√x+3 = 9x^2 -x-4

Giải chi tiết giúp tui nhe

Answer 1

a: ĐKXĐ: x>=2

Ta có: \(\sqrt{x-2}-\sqrt{x^2-4}\cdot3=0\)

=>\(\sqrt{x-2}-3\cdot\sqrt{x-2}\cdot\sqrt{x+2}=0\)

=>\(\sqrt{x-2}\left(1-3\sqrt{x+2}\right)=0\)

=>\(\left[\begin{array}{l}\sqrt{x-2}=0\\ 1-3\sqrt{x+2}=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x-2=0\\ 3\sqrt{x+2}=1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2\\ \sqrt{x+2}=\frac13\end{array}\right.\)

=>\(\left[\begin{array}{l}x=2\\ x+2=\frac19\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2\left(nhận\right)\\ x=-\frac{17}{9}\left(loại\right)\end{array}\right.\)

=>x=2