Question

log 3 (2x^2 -x-1)= log 3 (2x+1)

Answer 1

$\displaystyle\\\log_3 (2x^2 -x-1)= \log_3(2x+1)\\\\\Longrightarrow~~2x^2 -x-1=2x+1\\\\2x^2 -x-1-2x-1=0\\\\2x^2 -3x-2=0\\\\x_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{3\pm\sqrt{9+4\cdot 2}}{2}= \frac{3\pm\sqrt{9+8}}{2}=\frac{3\pm\sqrt{17}}{2}\\\\x_1 =\boxed{\bf \frac{3-\sqrt{17}}{2}}~~\text{Radacina respinsa fiind negativa.}\\\\x_2 =\boxed{\bf \frac{3+\sqrt{17}}{2}}$