Question

d, 8x³ -50x = 0      e, (4x-3)² - 3x (3-4x) = 0

Answer 1

d. 8x³ - 50x = 0

<=> 2x(4x - 25) = 0

<=> \(\left[{}\begin{matrix}2x=0\\4x-25=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=0\\x=\dfrac{25}{4}\end{matrix}\right.\)

e. (4x - 3)² - 3x(3 - 4x) = 0

<=> (4x - 3)² + 3x(4x - 3) = 0

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

<=> (4x - 3)(7x - 3) = 0

<=> \(\left[{}\begin{matrix}4x-3=0\\7x-3=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{3}{7}\end{matrix}\right.\)

Answer 2

d) \(8x^3-50x=0\Rightarrow2x\left(4x^2-25\right)=0\)  

   \(\Rightarrow2x\left(2x-5\right)\left(2x+5\right)=0\)

  \(\Rightarrow\left[{}\begin{matrix}2x=0\\2x+5=0\\2x-5=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\\x=\dfrac{5}{2}\end{matrix}\right.\)

e) \(\left(4x-3\right)^2-3x\left(3-4x\right)=0\) 

    \(\Rightarrow\left(4x-3\right)^2+3x\left(4x-3\right)=0\)

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

   \(\Rightarrow\left[{}\begin{matrix}4x-3=0\\7x-3=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{3}{7}\end{matrix}\right.\)