Найдите корни уравнения: (x-3)(x+3)=5x-13.

Ответ:

\[(x - 3)(x + 3) = 5x - 13\]

\[x^{2} - 9 - 5x + 13 = 0\]

\[x^{2} - 5x + 4 = 0\]

\[D = b^{2} - 4ac = 25 - 4 \cdot 1 \cdot 4 =\]

\[= 25 - 16 = 9\]

\[x_{1} = \frac{5 + 3}{2} = \frac{8}{2} = 4\]

\[x_{2} = \frac{5 - 3}{2} = \frac{2}{2} = 1\]

\[Ответ:x_{1} = 4;\ \ x_{2} = 1.\]