fie E(x)= (x+2)^2-(x-1)(x+1)-3(x+2), x€ R
a) sa se qrate ca E(x)= x-1
b) sa se calculeze s=E(1)+E(2)+E(3)+...+E(2022)​

Răspuns:

Explicație pas cu pas:

a) E(x) = (x+2)² - (x-1)(x+1) - 3(x+2) = x²+4x+4 - (x²-1) - 3x - 6 = x²+4x+4 - x² + 1 - 3x-6 = x-1

b) E(1) = 1-1 = 0

E(2) = 2-1 = 1

E(3) = 3-1 = 2

E(4) = 4-1 = 3

...........................

E(2020) = 2020-1 = 2019

E(2021) = 2021-1 = 2020

E(2022) = 2022-1 = 2021

=> E(0) + E(1) + E(2) + ... + E(2021) + E(2022) = 0+1+2+...+2020+2021 = [2021(2021+1)]:2 = 2021·2022:2 = 2021·1011 = 2 043 231