1) (3x²+4x) / (9-x) >0 2) log0.25 (3x-5) >-3 3) 2cos (x/2) + 1=0

1) (3x² + 4x) / (9 - x) > 0;

x (3x + 4) / (9 - x) > 0;

-3x (x + 4/3) / (x - 9) > 0;

x (x + 4/3) / (x-9) < 0;

x ∈ (-∞; - 4/3) ∪ (0; 9).

2) log₀,₂₅ (3x - 5) > - 3;

log₀,₂₅ (3x - 5) > log₀,₂₅ 0,25⁻³;

3x - 5 < 0,25⁻³ = 4 ³ = 64;

3x < 64 + 5 = 69;

x < 69 / 3 = 23;

x < 23.

3) 2cos (x/2) + 1 = 0;

2cos (x/2) = - 1;

cos (x/2) = - 1/2;

x/2 = ±arccos (-1/2) + 2πn, n целое;

x = ±2arccos (-1/2) + 4πn, n целое.

cos (x/2) = - 1;