Question

\(\left(x+3\right)\sqrt{5-x}-3=x\left(x+4\right)\)

Answer 1

ĐKXĐ: \(x\le5\)

\(x^2+4x+3-\left(x+3\right)\sqrt{5-x}=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+3\right)-\left(x+3\right)\sqrt{5-x}=0\)

\(\Leftrightarrow\left(x+3\right)\left(x+1-\sqrt{5-x}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\\sqrt{5-x}=x+1\left(x\ge-1\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\5-x=x^2+2x+1\left(x\ge-1\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)

Answer 2

(x + 3)\(\sqrt{5-x}-3=x\left(x+4\right)\) ĐKXĐ: x > 5

<=> \(\sqrt{5-x}-3=x^2+4x-x-3\)

<=> \(\sqrt{5-x}=x^2+3x\)

<=> 5 - x = (x² + 3x)²

<=> 5 - x = x⁴ + 6x³ + 9x²

<=> x⁴ + 6x³ + 9x² + x - 5 = 0

<=> x = 0,586