Question

Giai phuong trinh: \(\sqrt{2x-1}-2\sqrt{x-1}=-1\)

Answer 1

Đk x >= 1

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

Bình phương 2 vế ta có :

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

=> 2x - 1 = 4x - 4 + 1 - 4 căn( x - 1)

=> 2x - 1 = 4x - 3 - 4 căn ( x - 1)

=> 4 căn ( x - 1) = 2x - 2 

=> 2 can ( x - 1)  = x - 1

=> 4 ( x - 1)  = x^2 - 2x + 1

=> 4x - 4 - x^2 + 2x - 1 = 0

=> -x^2 + 6x - 5   = 0

=> x^2 - 6x + 5  = 0 

=> x = 1  hoặc  x = 5