Question

a) 1/2 * sqrt(x - 1) - sqrt(4x - 4) + 3 = 0  c) sqrt(7 - x + 1) = x b) sqrt(x ^ 2 - 4x + 4) + x - 2 = 0

Answer 1

a: ĐKXĐ: x>=1

\(\dfrac{1}{2}\sqrt{x-1}-\sqrt{4x-4}+3=0\)

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

=>\(3-\dfrac{3}{2}\sqrt{x-1}=0\)

=>\(\dfrac{3}{2}\sqrt{x-1}=3\)

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

=>x-1=4

=>x=5(nhận)

b: \(\sqrt{x^2-4x+4}+x-2=0\)

=>\(\sqrt{\left(x-2\right)^2}=-x+2\)

=>|x-2|=-(x-2)

=>x-2<=0

=>x<=2

c: 

ĐKXĐ: 7-x>=0

=>x<=7

\(\sqrt{7-x}+1=x\)

=>\(\sqrt{7-x}=x-1\)

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

=>\(\left\{{}\begin{matrix}1< =x< =7\\x^2-x-6=0\end{matrix}\right.\Leftrightarrow x=3\)