Question

a.) S= (-3)+(-2)+(-1)...... +(+25) + (+26)+(+27)=


b.) Daca |2z-1|=3 si z ∈Z , atunci z∈............

Answer 1

a) S = -(3+2+1) + 0 + 1+2+...+27 = 
= -6 + (27*28):2 = -6 + 27 * 14 = -6 +378 = 372
b) |2z-1| = 3 => 
I) 2z - 1 = 3 sau
II) 2z - 1 = -3
I) 2z - 1 =3 => 2z = 4 => z = 2
II) 2z - 1 = -3 => 2z = -3+1 = -2 => z = -1
=> z ∈{2, -1}

Answer 2

$a)~S=(1+2+3+...+27)-(1+2+3)= \\ ~~~~~~~= \frac{27*28}{2}-6= \\ ~~~~~~~=27*14-6= \\ ~~~~~~~= 372.$

$b)~|2z-1|=3 \Rightarrow~2z-1=3~sau~2z=1=-3. \\ \\ 2z-1=3 \Rightarrow 2z=4 \Rightarrow z=2. \\ 2z-1=-3 \Rightarrow 2z=-2 \Rightarrow z=-1. \\ \\ \underline{Solutie}: \boxed{x \in \{-1;2\}}.$