Решите неравенство: x^3-10x^2+21x>=0.

Ответ:

\[x^{3} - 10x^{2} + 21x \geq 0\]

\[x\left( x^{2} - 10x + 21 \right) \geq 0\]

\[x^{2} - 10x + 21 = 0\]

\[D_{1} = 25 - 21 = 4\]

\[x_{1} = 5 + 2 = 7;\ \ x_{2} = 5 - 2 = 3.\]

\[x(x - 3)(x - 7) \geq 0\]

\[0 \leq x \leq 3;\ \ x \geq 7.\]