Question

Answer 1

`ĐKXĐ: x >= -2`

\(\sqrt{4x+8}+\dfrac{1}{2}\sqrt{x+2}+3\sqrt{9x+18}=23\\ \Leftrightarrow\sqrt{4\left(x+2\right)}+\dfrac{1}{2}\sqrt{x+2}+3\sqrt{9\left(x+2\right)}=23\\ \Leftrightarrow\sqrt{4}.\sqrt{x+2}+\dfrac{1}{2}\sqrt{x+2}+3\sqrt{9}.\sqrt{x+2}=23\\ \Leftrightarrow2\sqrt{x+2}+\dfrac{1}{2}\sqrt{x+2}+3.3.\sqrt{x+2}=23\\ \Leftrightarrow2\sqrt{x+2}+\dfrac{1}{2}\sqrt{x+2}+9\sqrt{x+2}=23\\ \Leftrightarrow\left(2+\dfrac{1}{2}+9\right)\sqrt{x+2}=23\)

\(\Leftrightarrow\dfrac{23}{2}\sqrt{x+2}=23\\ \Leftrightarrow\sqrt{x+2}=2\\ \Leftrightarrow x+2=4\\ \Leftrightarrow x=2\left(tm\right)\)

Vậy pt có tập nghiệm `S={2}`