Question

a) 5x(x – 2000) – x + 2000 = 0   b) 5x2 = 13x

c) x3+2x=0                                  d) x(x-5)= 5-x

Answer 1

a) \(5x\left(x-2000\right)-x+2000=0\)

\(\Leftrightarrow5x\left(x-2000\right)-\left(x-2000\right)=0\)

\(\Leftrightarrow\left(5x-1\right)\left(x-2000\right)=0\)

\(\Leftrightarrow x\in\left\{\frac{1}{5};2000\right\}\)

Answer 2

\(5x^2=13x\)

\(\Leftrightarrow x\left(5x-13\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{13}{5}\end{cases}}\)

Answer 3

c) \(x^3+2x=0\)

\(\Leftrightarrow x\left(x^2+2\right)=0\)

\(\Leftrightarrow x=0\)

Answer 4

d) \(x\left(x-5\right)=5-x\)

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

\(\Leftrightarrow x=1,x=5\)