Question

1)3х^2-11х-4<0
2)х^2-14х+40 больше 0
3)(х+3)(х+8)(х-20) больше 0
решите неравенство

Answer 1

1.

$3x^{2} - 11x < 0 \\ 3x^{2} - 11x = 0 \\ x \times (3x - 11) = 0 \\ x = 0 \\ 3x - 11 = 0 \\ 3x = 11 \\ x = 11 \div3 \\ x = \frac{11}{3}$

2.

$x^{2} - 14x + 4 > 0 \\ x {}^{2} - 14x + 4 = 0 \\ d = (- 14)^{2} - 4 \times 1 \times 4 = 180 = \sqrt{180} \\ x1 = \frac{14 + \sqrt{180} }{2} = 7 + 3 \sqrt{5} \\ x2 = \frac{14 - \sqrt{180} }{2} = 7 - 3 \sqrt{5}$

3.

$(x + 3) \times (x + 8) \times (x - 20) > 0 \\ x + 3 = 0 \\ x = - 3 \\ x + 8 = 0 \\ x = - 8 \\ x - 20 = 0 \\ x = 20$