Question

Решите неравенства:
1) 13 + x² ( x - 9 ) ⩽ ( x - 3 )³ + 11
2) 26 + ( 2 + x )³ < x² ( 6 + x )

Answer 1

1)13+x²(x-9)≤(x-3)³+11
13+x³-9x²≤x³-3*x²*3+3*x*3²-3³
13+x³-9x²≤x³-9x²+27x-27
x³-9x²-x³+9x²-27x≤-27-13
-27x≤-40
x≤1 13/27
(-∞;1 13/27]
2)26+(2+x)³26+2³+3*2²*x+3*2*x²+x³<6x²+x³
26+8+12x+6x²+x³<6x²+x³
12x+6x²+x³-6x²-x³<-26-8
12x<-34
x<-2 10/12
(-∞;-2 10/12)