Question

\(3\sqrt{\dfrac{4x+8}{9}}-\sqrt{9x+18}=3-4\sqrt{x+2}\)

Answer 1

đề bài mình có lỗi không hay gì mà mn k chả lời =(

Answer 2

x= -1.

Answer 3

\(3\sqrt{\dfrac{4x+8}{9}}-\sqrt{9x+18}=3-4\sqrt{x+2}\)

\(\Leftrightarrow\sqrt{4\left(x+2\right)}-\sqrt{9\left(x+2\right)}=3-4\sqrt{x+2}\)

\(ĐK:x\ge-2\)

Đặt \(x+2=a;a\ge0\)

pt trở thành:

\(\Leftrightarrow\sqrt{4a}-\sqrt{9a}=3-4\sqrt{a}\)

\(\Leftrightarrow2\sqrt{a}-3\sqrt{a}=3-4\sqrt{a}\)

\(\Leftrightarrow3\sqrt{a}-3=0\)

\(\Leftrightarrow\sqrt{a}-1=0\)

\(\Leftrightarrow a=1\left(tm\right)\)

\(\Rightarrow x+2=1\)

\(\Leftrightarrow x=-1\left(tm\right)\)

Vậy \(S=\left\{-1\right\}\)