1. an=a1+d(n-1);
a6=1/3+1/4*(6-1)=1/3+1/4*5=1/3+5/4=4/12+15/12=19/12;
2. Sn=((2a1+d(n-1))/2)*n;
S51=((2*3,5+0,2(51-1))/2)*51=((7+0,2*50)/2)*51=((7+10)/2)*51=8,5*51=433,5;
(-5a³b⁴)² * (- 0,2ab²)² = 25a⁶b⁸ * 0,04a²b⁴ = a⁶⁺²b⁸⁺⁴ = a⁸b¹²
1) (х+1)(х²-х+1)-х(х²+4) ≤ 9
х³+1-х³-4х ≤ 9
-4х ≤ 8
х ≥ -2
--------------.-------------->x
-2//////////////////
2) (х-3)/5 > (х+5)/3
3(х-3) > 5(x+5)
3x-9 > 5x+25
-2x > 34
x < -17
--------------₀------------>x
\\\\\\\\\\\\\\\-17
3) ----------₀-----------.----------->x
\\\\\\\\\\\\\-17 -2////////////////
Общих решений нет!
Ответ: система не имеет решений