PT<=>\(\sqrt{5x+7}=4\sqrt{x+3}\)
<=> \(\begin{cases}x\ge-\frac{7}{4}\\5x+7=16x+48\end{cases}\)
<=> \(\begin{cases}x\ge-\frac{7}{4}\\x=-\frac{41}{11}\end{cases}\)
=> PTVN
\(ĐK:\begin{cases}5x+7\ge0\\x+3>0\end{cases}\) \(\Leftrightarrow\begin{cases}x\ge-\frac{7}{5}\\x>-3\end{cases}\) \(\Leftrightarrow x\ge-\frac{7}{5}\)
\(\frac{\sqrt{5x+7}}{\sqrt{x+3}}=4\)
\(\Leftrightarrow\)\(\frac{5x+7}{x+3}=16\)
\(\Leftrightarrow16\left(x+3\right)=5x+7\)
\(\Leftrightarrow16x+48=5x+7\)
\(\Leftrightarrow16x-5x=7-48\)
\(\Leftrightarrow11x=-41\)
\(\Leftrightarrow x=\frac{-41}{11}\left(KTM\right)\)
Vậy pt vô nghiệm
\(\frac{\sqrt{5x+7}}{\sqrt{x+3}}\) = 4 (1)
đkxđ: \(\begin{cases}5x+7\ge0\\x+3\ge0\end{cases}\Leftrightarrow\begin{cases}x\ge\frac{7}{5}\\x\ge-3\end{cases}}\)
(1) \(\Leftrightarrow\) \(\frac{5x+7}{x+3}\)= 16
\(\Leftrightarrow\) 5x +7 = 16x+48
\(\Leftrightarrow\) x = \(\frac{-41}{11}\) (L)
Vậy pt vô nghiệm
đkxđ : \(\begin{cases}5x+7\ge0\\x+3>0\end{cases}\) <=> \(\begin{cases}x\ge\frac{-7}{5}\\x>-3\end{cases}\) <=> x \(\ge\) \(\frac{-7}{5}\)
