Решите уравнение: x^2-10x+25+|x^2-9x+20|=0.

Ответ:

\[(x - 5)^{2} + \left| x^{2} - 9x + 20 \right| = 0\]

\[(x - 5)^{2} \geq 0;\ \ \ \ \]

\[\left| x^{2} - 9x + 20 \right| \geq 0 \Longrightarrow сумма\ \]

\[равна\ 0,\ если\ оба\ \]

\[выражения\ равны\ 0.\]

\[x - 5 = 0\]

\[x = 5.\]

\[x^{2} - 9x + 20 = 0\]

\[D = ( - 9)^{2} - 4 \cdot 1 \cdot 20 =\]

\[= 81 - 80 = 1\]

\[x_{1} = \frac{9 + \sqrt{1}}{2} = \frac{9 + 1}{2} = \frac{10}{2} = 5\]

\[x_{2} = \frac{9 - \sqrt{1}}{2} = \frac{9 - 1}{2} = \frac{8}{2} = 4\]

\[Ответ:x = 5.\]