Question

(5x - 1)² = (3 - 4x)²

Answer 1

\(\left(5x-1-3+4x\right)\left(5x-1+3-4x\right)=0\)

\(\left(9x-4\right)\left(x+2\right)=0\)

\(\left[{}\begin{matrix}9x-4=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{9}\\x=-2\end{matrix}\right.\)

Answer 2

(5x - 1)² = (3 - 4x)²

<=> (5x - 1)² - (3 - 4x)² = 0

<=> (5x - 1 + 3 - 4x)(5x - 1 - 3 + 4x) = 0

<=> (x + 2)(9x - 4) = 0

<=> \(\left[{}\begin{matrix}x+2=0\\9x-4=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=-2\\x=\dfrac{4}{9}\end{matrix}\right.\)

Answer 3

\(\Leftrightarrow\left(5x-1-3+4x\right)\left(5x-1+3-4x\right)=0\\ \Leftrightarrow\left(9x-4\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{9}\\x=-2\end{matrix}\right.\)

Answer 4

\(\Leftrightarrow\left(5x-1-4x+3\right)\left(5x-1+4x-3\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(9x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{4}{9}\end{matrix}\right.\)

Answer 5

=>(5x-1)²-(3-4x)²=0
=>(5x-1-3+4x)(5x-1+3-4x)=0
=>(9x-4)(x+2)=0
=>\(\left\{{}\begin{matrix}9x-4=0\\x+2=0\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x=\dfrac{4}{9}\\x=-2\end{matrix}\right.\)