Question

(2x+14)\(\sqrt{x+5}\)=x²+15x+38 . Giải pt

Answer 1

Pls help nhanh , tui cần gấp lắm ;-;

Answer 2

ĐKXĐ: \(x\ge-5\)

\(\Leftrightarrow\left(x+7\right)^2-2\left(x+7\right)\sqrt{x+5}+x+5-16=0\)

\(\Leftrightarrow\left(x+7-\sqrt{x+5}\right)^2-16=0\)

\(\Leftrightarrow\left(x+7-\sqrt{x+5}-4\right)\left(x+7-\sqrt{x+5}+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+5}=x+3\left(x\ge-3\right)\\\sqrt{x+5}=x+11\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=x^2+6x+9\\x+5=x^2+22x+121\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+5x+4=0\\x^2+21x+116=0\left(vn\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4< -3\left(l\right)\end{matrix}\right.\)