Question

Find the roots of x2-2x-(r2-1)

Answer 1

${x}^{2} - 2x - ( {r}^{2} - 1) = 0 \\ \\ \Rightarrow {x}^{2} - 2x - {r}^{2} + 1 = 0 \\ \\ \Rightarrow {x}^{2} - 2x + 1 - {r}^{2} = 0 \\ \\ \Rightarrow {(x - 1)}^{2} - {r}^{2} = 0 \\ \\ \Rightarrow (x - 1 + r)(x - 1 - r) = 0$

$1. \\ x - 1 + r = 0 \\ x = 1 - r \\ \\ 2. \\ x - 1 - r= 0 \\ x = 1 + r$

$\boxed{\textbf{roots are: (1+r) and (1-r)}}$