Question

giup mik zoi

Answer 1

\(ĐKXĐ:x\ge-5\)

\(3\sqrt{4x+20}+12\sqrt{\dfrac{x+5}{9}}=2+\sqrt{16x+80}\)

\(\Leftrightarrow3\sqrt{4\left(x+5\right)}+12\sqrt{\dfrac{1}{9}\left(x+5\right)}=2+\sqrt{16\left(x+5\right)}\)

\(\Leftrightarrow6\sqrt{x+5}+4\sqrt{x+5}=2+4\sqrt{x+5}\)

\(\Leftrightarrow6\sqrt{x+5}=2\)

\(\Leftrightarrow\sqrt{x+5}=\dfrac{1}{3}\Leftrightarrow x+5=\dfrac{1}{9}\Leftrightarrow x=-\dfrac{44}{9}\) (TMĐK)

Vậy \(S=\left\{-\dfrac{44}{9}\right\}\).

Answer 2

`3\sqrt{4x+20}+12\sqrt{[x+5]/9}=2+\sqrt{16x+80}`      `ĐK: x >= -5`

`<=>6\sqrt{x+5}+4\sqrt{x+5}=2+4\sqrt{x+5}`

`<=>6\sqrt{x+5}=2`

`<=>\sqrt{x+5}=1/3`

`<=>x+5=1/9`

`<=>x=46/9` (t/m)

Vậy `S={46/9}`