1) f(x)+3g(x)+3x-2=х³+3(х²+1)+3х-2=
=х³+3х²+3+3х-2=х³+3х²+3х+1.
2) g( f(x))=(х³)²+1=х^6+1.
t² + 5t + 6 = 15* (t² +3t +6)/(t²+t) | * (t² +t)
(t² + 5t + 6)<u>(t² +t)</u> = 15*(t² +3t +6)
(t + 2)(t + 3) <u>t(t + 1)</u> = 15*(t² +3t +6)
(t+2)(t+1) *t *(t+3) = 15*(t² +3t +6)
(t² +3t +2)(t² +3t) = 15*(t² +3t +6)
t² +3t = z
(z+2)*z = 15*(z +6)
z² +2z = 15z +90
z² -13z -90 = 0
корни по т. Виета 18 и -5
а) z = 18 б) z = -5
t² +3t = 18 t² +3t = -5
t² +3t -18 = 0 t² +3t + 5 = 0
по т. Виета D < 0
корни -6 и 3 ∅
Ответ : -6 и 3
1. 1/81;27
2. (-2;1)
3. 1/243.