Question

\(2x+\sqrt{2-x}-1=0\)

Answer 1

\(\sqrt{2-x}=1-2x\) với x</ 1/2

=>2-x = 1-4x +4x² => 4x² -3x-1=0 => (x-1)(4x+1)=0

=> x =1 loại

=> x =-1/4 TM

Vậy x =-1/4

Answer 2

\(x\le2\)

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

\(\Rightarrow2-x=1-4x+4x^2\)

\(\Rightarrow4x^2-3x-1=0\)

\(\Rightarrow4x^2-4x+x-1=0\)

\(\Rightarrow4x\left(x-1\right)+\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left(4x+1\right)=0\)

=> x - 1 = 0 => x = 1 (nhận)

hoặc 4x + 1 = 0 => x = -1/4 (nhận)

Vậy x = -1/4 ; x = 1