Question

E(x)=(x²+x-1)²-(x²-2)²-2x(x-1)(x+1)+3, unde x€ R
a) arătați că E(x)=3x²
b) calculați E(2-√3)-E(2+√3)
ESTE LA MATEMATICĂ SCUZE

Answer 1

E(x)=(x²+x-1)²-(x²-2)²-2x(x-1)(x+1)+3
E(x)=(x²+x-1-x²+2)(x²+x-1+x²-2)-2x(x-1)(x+1)+3
E(x)=(x+1)(2x²+x-3)-(2x²-2x)(x+1)+3
E(x)=(x+1)(3x-3)+3
E(x)=3(x+1)(x-1)+3
E(x)=3x²-3+3
E(x)=3x²

E(2-√3)-E(2+√3)= 3(2-√3)²-3(2+√3)² 
=3(2-√3-2-√3)(2-√3+2+√3)=-24√3