Question

Решите неравенство:
а) 5y²-5y(y+4)≥100
б) 6а(а-1)-2а(3а-2)<6
в) 0,2х²-0,2(х-6)(х+6)>3,6х
г) (2х-5)²-0,5х<(2х-1)(2х+1)-15

Answer 1

Ответ:
а) y ≤ -5
б) a > - 3/4
в) x < 2
г) x > 2

Answer 2

Ответ:a) \(5y^2 - 5y(y+4) \geq 100\):

\[5y^2 - 5y^2 - 20y \geq 100\]

\[ -20y \geq 100\]

\[y \leq -5\]

b) \(6a(a-1) - 2a(3a-2) < 6\):

\[6a^2 - 6a - 6a^2 + 4a < 6\]

\[-2a < 6\]

\[a > -3\]

c) \(0.2x^2 - 0.2(x-6)(x+6) > 3.6x\):

\[0.2x^2 - 0.2(x^2 - 36) > 3.6x\]

\[0.2x^2 - 0.2x^2 + 7.2 > 3.6x\]

\[7.2 > 3.6x\]

\[x < 2\]

d) \((2x-5)^2 - 0.5x < (2x-1)(2x+1) - 15\):

\[4x^2 - 20x + 25 - 0.5x < 4x^2 - 1 - 15\]

\[-20.5x + 25 < -16\]

\[-20.5x < -41\]

\[x > 2\]

Объяснение: