Răspuns :
Răspuns:
E(x) =4x^2-4x+1-3(x^2-x-6) - x^2+x+2
E(x) =4x^2-4x+1-3x^2+3x+18-x^2+x+2
E(x) =21
21x2020=42420
[tex]\it E(x)=(2x-1)^2-3(x-3)(x+2)-(x-2)(x+1)=\\ \\ =4x^2-4x+1-3(x^2+2x-3x-6)-(x^2+x-2x-2)=\\ \\ =4(x^2-x)+1-3(x^2-x-6)-(x^2-x-2)[/tex]
[tex]\it Not\breve am\ \ x^2-x=t, iar\ expresia\ devine:\\ \\ E=4t+1-3t+18-t+2=21\\ \\ Deci, E(x)=21,\ \ \forall\ x\in\mathbb{R}[/tex]
[tex]\it E(1) +E(\dfrac{1}{2})+E(\dfrac{1}{3})+\ ...\ +E(\dfrac{1}{2020})=\underbrace{21+21+21+\ ...\ +21}_{2020\ termeni}=\\ \\ \\ =2020\cdot21=42420[/tex]