Question

\(\dfrac{3x+2}{\sqrt{x+2}}=2\sqrt{x+2}\)

Giải phương trình

Answer 1

ĐK: x > -2

\(\dfrac{3x+2}{\sqrt{x+2}}=2\sqrt{x+2}\Leftrightarrow3x+2=2\left(x+2\right)\Leftrightarrow3x+2=2x+4\Leftrightarrow3x-2x=4-2\Leftrightarrow x=2\left(tm\right)\)

Vậy x = 2

Answer 2

\(\dfrac{3x+2}{\sqrt{x+2}}=2\sqrt{x+2}\) . ĐKXĐ : \(x>-2\)

\(\Leftrightarrow\) \(\dfrac{3x+2}{\sqrt{x+2}}=\dfrac{2\sqrt{x+2}.\sqrt{x+2}}{\sqrt{x+2}}\)

\(\Leftrightarrow3x+2=2x+4\)

\(\Leftrightarrow x=2\) ( Thỏa mãn )

Vậy \(S=\left\{2\right\}\)

Answer 3

\(\dfrac{3x+2}{\sqrt{x+2}}=2\sqrt{x+2}\left(x>-2\right)\)

⇔ \(3x+2=2\left(x+2\right)\)

⇔ \(3x+2=2x+4\)

⇔ \(x=2\left(TM\right)\)

KL.........

Answer 4

\(\dfrac{3x+2}{\sqrt{x+2}}=2\sqrt{x+2}\\ \Leftrightarrow3x+2=2\left(x+2\right)\\ \Leftrightarrow3x+2=2x+4\\ \Leftrightarrow3x-2x=4-2\\ \Leftrightarrow x=2\)

Vậy......