Question

  …….

Answer 1

\(a)\sqrt{x+5}-\dfrac{1}{4}\sqrt{9x+45}+\sqrt{4x+20}=18\\ \Leftrightarrow\sqrt{x+5}-\dfrac{1}{4}\sqrt{9\left(x+5\right)}+\sqrt{4\left(x+5\right)}=18\\ \Leftrightarrow\sqrt{x+5}-\dfrac{3}{4}+2\sqrt{x+5}=18\\ \Leftrightarrow\dfrac{9}{4}\sqrt{x+5}=18\\ \Leftrightarrow\sqrt{x+5}=8\left(ĐK:x\ge-5\right)\\ \Leftrightarrow x+5=64\\ \Leftrightarrow x=64-5\\ \Leftrightarrow x=59\left(tm\right)\\ Vậy.S=\left\{59\right\}\)

\(b)\sqrt{x^2-6x+9}-2=0\\ \Leftrightarrow\sqrt{\left(x-3\right)^2}=2\\ \Leftrightarrow\left|x-3\right|=2\\ \Leftrightarrow\left[{}\begin{matrix}x-3=2\left(ĐK:x\ge3\right)\\x-3=-2\left(ĐK:x< 3\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2+3\\x=-2+3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\left(tm\right)\\x=1\left(tm\right)\end{matrix}\right.\\ Vậy.S=\left\{1;5\right\}\)

\(c)ĐK:x\ne1;x\ge0\\ \dfrac{x+1}{\sqrt{x}-1}=5\\ \Leftrightarrow5\left(\sqrt{x}-1\right)=x+1\\ \Leftrightarrow5\sqrt{x}-5=x+1\\ \Leftrightarrow5\sqrt{x}-x=1+5\\ \Leftrightarrow5\sqrt{x}-x=6\\ \Leftrightarrow5\sqrt{x}=x+6\\ \Leftrightarrow25x=x^2+12x+36\\ \Leftrightarrow x^2+12x-25x+36=0\\ \Leftrightarrow x^2-13x+36=0\\ \Leftrightarrow\left[{}\begin{matrix}x=9\left(tm\right)\\x=4\left(tm\right)\end{matrix}\right.\\ Vậy.S=\left\{4;9\right\}\)