Question

Se da expresia:E(x)=(x²+x-1)²-(x²-2)²-2x(x-1)(x+1)+3,unde x apartine lui R:
a) aratati ca E(x) =3x²
b) calculati E(2-√3)-E(2+√3)
Urgent!

Answer 1

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

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