Question

РЕШИТЕ НЕРАВЕНСТВО x²(x-1)/x²-14x+48<_0
СРОЧНО ДАМ 100 БАЛОВ​

Answer 1

$\frac{ {x}^{2}(x - 1) }{ {x}^{2} - 14x + 48 } \leqslant 0$

${x}^{2} - 14x + 48 = 0$

По теореме Виета:

${x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c$

$x_{1} + x_{2} = 14 \\ x_{1} x_{2} =48 \\ x_{1} = 6 \\ x_{2} = 8 \\ \\ {ax}^{2} + bx + c = a(x - x_{1})(x - x_{2}) \\ {x}^{2} - 14x + 48 = (x - 6)(x - 8)$

$\frac{ {x}^{2} (x - 1)}{(x - 6)(x - 8)} \leqslant 0 \\ \\ \left \{ {{ {x}^{2} (x - 1)(x - 6)(x - 8) \leqslant 0} \atop {x\neq6 \: \: \: \: \: \: \: x\neq8 }} \right. \\ \\ - - - [0] - - - [1] + + + (6) - - - (8) + + + \\ x \:\epsilon \: ( - \propto; \: 1]U(6; \: 8)$