Question

  ……..

Answer 1

a: ĐKXĐ: x>=0

\(2\sqrt{8x}+7\sqrt{18x}=9-\sqrt{50x}\)

=>\(4\sqrt{2x}+21\sqrt{2x}=9-5\sqrt{2x}\)

=>\(25\sqrt{2x}+5\sqrt{2x}=9\)

=>\(30\sqrt{2x}=9\)

=>\(\sqrt{2x}=\dfrac{3}{10}\)

=>2x=9/100

=>x=9/200(nhận)

b: ĐKXĐ: x>=-2

\(\sqrt{9x+18}-2\sqrt{x+2}=35\left(5-\dfrac{1}{2}\sqrt{4x+8}\right)\)

=>\(3\sqrt{x+2}-2\sqrt{x+2}=175-35\cdot\dfrac{1}{2}\cdot2\sqrt{x+2}\)

=>\(\sqrt{x+2}+35\sqrt{x+2}=175\)

=>\(36\sqrt{x+2}=175\)

=>\(x+2=\left(\dfrac{175}{36}\right)^2=\dfrac{30625}{1296}\)

=>\(x=\dfrac{28033}{1296}\)

c: ĐKXĐ: \(x\in R\)

\(2\sqrt{\left(x-4\right)^2}-6=0\)

=>\(2\left|x-4\right|-6=0\)

=>|x-4|=3

=>\(\left[{}\begin{matrix}x-4=3\\x-4=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=1\end{matrix}\right.\)

d: ĐKXĐ: \(\left\{{}\begin{matrix}2x-1>=0\\x+3>=0\end{matrix}\right.\)

=>x>=1/2

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

=>2x-1=x+3

=>x=4(nhận)