Question

Consideram expresia:
E(x)= 2x-1 totul la puterea 2 + 2(2x-1)(2-x)+2x-1totul la puterea 2
a)Aratati ca E(x)=x+1totul la puterea 2
b)Calculati: E(Radical din 2)*E(-radical din 2)

Answer 1

a)
E(x)= 2x-1 totul la puterea 2 + 2(2x-1)(2-x)+2-xtotul la puterea 2

2x-1=y si 2-x=z

E(x)=y^2 +2yz +z^2=(y^2+yz)+(yz+z^2)=y(y+z)+z(y+z)=(y+z)(y+z)=(y+z)^2

Inlocuim: E(x)=(2x-1+2-x)^2=(x+1)^2

b)
''V''=radical

E(V2)*E(-V2)=[(V2)+1]^2 *[(-V2)+1]^2=(2+2V2+1)*(2-2V2+1)=

(3+2V2)(3-2V2)=9-8=1