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.

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