( 5x + 1 )2 = 36/49
<=> ( 5x + 1 )2 = ( ±6/7 )2
<=> 5x + 1 = 6/7 hoặc 5x + 1 = -6/7
<=> x = -1/35 hoặc x = -13/35
\(\left(5x+1\right)^2=\frac{36}{49}\)
\(\Rightarrow\orbr{\begin{cases}5x+1=\frac{6}{7}\\5x+1=\frac{-6}{7}\end{cases}}\)\(\)
\(\Rightarrow\orbr{\begin{cases}5x=\frac{-1}{7}\\5x=\frac{-13}{7}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-1}{35}\\x=\frac{-13}{35}\end{cases}}\)
\(\left(5x+1\right)=\pm\sqrt{\frac{36}{49}}=\pm\frac{6}{7}\)
\(\orbr{\begin{cases}5x+1=\frac{6}{7}\\5x+1=-\frac{6}{7}\end{cases}}\)
\(\orbr{\begin{cases}5x=\frac{-1}{7}\\5x=\frac{-13}{7}\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{-1}{35}\\x=\frac{-13}{35}\end{cases}}\)
Bài làm:
Ta có: \(\left(5x+1\right)^2=\frac{36}{49}\)
\(\Leftrightarrow\left(5x+1\right)^2-\left(\frac{6}{7}\right)^2=0\)
\(\Leftrightarrow\left(5x+\frac{1}{7}\right)\left(5x+\frac{13}{7}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}5x+\frac{1}{7}=0\\5x+\frac{13}{7}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}5x=-\frac{1}{7}\\5x=-\frac{13}{7}\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{35}\\x=-\frac{13}{35}\end{cases}}\)
