1) х²-6х <0<br> x²-6x+9
x(x-6) <0<br> (x-3)²
{x(x-6)(x-3)(x-3)<0<br>{x≠3
x(x-6)(x-3)(x-3)<0<br>x=0 x=6 x=3
+ - - +
------ 0 --------- 3 ----------- 6 --------
\\\\\\\\\\ \\\\\\\\\\\
x∈(0; 3)∨(3; 6)
2) х²+9х+20>0
x+4
Разложим х²+9х+20 на множители:
х²+9х+20=0
Д=81-80=1
х₁=-9-1=-5
2
х₂=-9+1=-4
2
х²+9х+20=(х+5)(х+4)
(х+5)(х+4)>0
x+4
x+5>0
{x+5>0
{x≠-4
x+5>0
x>-5
\\\\\\\\ \\\\\\\\\\\\\\\\\
------ -5 ------- -4 ------------
x∈(-5; -4)∨(-4; +∞)