Question

Se considera expresia E(x) = (x²-x+2)² - (x²-x)² - (2x-1)² , undex apartine R. Demonstrati ca E(x) = 3, oricare ar fi x apartine R.

Answer 1

pai...
(x²-x+2)² = (x²)²+x²+2²-2x²×x+2x²×2-2x×2=x⁴+x²+4-2x³+4x²-4x
(x²-x)²= (x²)²-2x²×x+x²=x⁴-2x³+x²
(2x-1)²=(2x)²-2×2x×1+1²=4x²-4x+1

acum expresia va fi
E(x) = (x²-x+2)² - (x²-x)² - (2x-1)² 
E(x)=x⁴+x²+4-2x³+4x²-4x -(x⁴-2x³+x²)-(4x²-4x+1)
E(X)=x⁴+x²+4-2x³+4x²-4x -x⁴+2x³-x²-4x²+4x-1
pe cele care se anuleaza le ingros ca sa iti fie mai simplu
E(X)=+x²+4-2x³+4x²-4x+2x³-x²-4x²+4x-1
E(X)=+4-2x³-4x+2x³+4x-1
E(X)=4-4x+4x-1
E(X)=4-1
E(X)=3