Question

chỉ cần làm những câu đánh dấu thôi ạ

Answer 1

Bài 9:

1: ĐKXĐ: x>=0

\(\sqrt{2x}=\sqrt{x+5}\)

=>2x=x+5

=>2x-x=5

=>x=5(nhận)

2: ĐKXĐ: x>=1

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

=>2x-1=x-1

=>2x-x=-1+1

=>x=0(loại)

6: ĐKXĐ: \(\left\{{}\begin{matrix}x^2-x>=0\\3x-5>=0\end{matrix}\right.\)

=>\(x>=\dfrac{5}{3}\)

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

=>\(x^2-x=3x-5\)

=>\(x^2-4x+5=0\)

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

=>\(\left(x-2\right)^2+1=0\)(vô lý)

=>\(x\in\varnothing\)

Bài 10:

1: ĐKXĐ: x>=5

\(\sqrt{x^2-25}-\sqrt{x-5}=0\)

=>\(\sqrt{x-5}\left(\sqrt{x+5}-1\right)=0\)

=>\(\left[{}\begin{matrix}x-5=0\\x+5=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\left(nhận\right)\\x=-4\left(loại\right)\end{matrix}\right.\)

2: ĐKXĐ: x>=2

\(\sqrt{x^2-4}-3\sqrt{x-2}=0\)

=>\(\sqrt{x-2}\cdot\sqrt{x+2}-\sqrt{x-2}\cdot3=0\)

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

=>\(\left[{}\begin{matrix}x-2=0\\x+2=9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(nhận\right)\\x=7\left(nhận\right)\end{matrix}\right.\)

Bài 11:

1: ĐKXĐ: x>=2

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

=>\(x-2-\sqrt{x-2}=4-2=2\)

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

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

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

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

=>x-2=4

=>x=4+2=6(nhận)

2: ĐKXĐ: x>=-2

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

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

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

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

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

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

=>x+2=1

=>x=-1(nhận)

3: ĐKXĐ: x>=2

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

=>\(x-2-5\sqrt{x-2}+6=0\)

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

=>\(\left[{}\begin{matrix}\sqrt{x-2}-3=0\\\sqrt{x-2}-2=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x-2=9\\x-2=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9+2=11\left(nhận\right)\\x=4+2=6\left(nhận\right)\end{matrix}\right.\)