1. (3x^2 + 4x) / (9-x) > 0; 8(-1) <0;<br>3x(x+4) / ( x - 9 ) < 0;
x = 0;
x = - 4;
x = 9
- + - +
_____(-4)____(0)_______9______x
x ∈( - ∞; -4) U (0; 9).
2. log0,25_(3x - 5) > - 3;
- log4_(3x - 5) > - 3; *(-1) < 0;
log4_(3x - 5) < 3;
log4_(3x - 5) < log4_(4^3);
4 > 1;⇒
3x - 5 < 64;
3x < 69;
x < 23;
x∈(- ∞; 23).
3. 2 cos (x/2) + 1 = 0;
cos(x/2) = -1/2;
x/2 = + - arccos(-1/2) + 2pi*k;
x/2 = + - 2pi/3 + 2 pi*k; *2
x = + - 4 pi/3 + + 4 *pi*k; k -Z