[tex]E(x)=(x+1)^{2} +2(x+1)(x-2)+(x-2)^{2}[/tex]
[tex]E(x)=x^{2}+2x+1 +(2x+2)(x-2)+x^{2} -4x+4[/tex]
[tex]E(x)=x^{2}+2x+1 +2x^{2}-4x+2x-4 +x^{2} -4x+4[/tex]
[tex]E(x)=4x^{2} -4x+1[/tex]
[tex]E(x)=(2x-1)^{2}[/tex]
Răspuns:
Explicație pas cu pas:
E₍ₓ₎=(x+1)²+2(x+1)(x-2)+(x-2)²
E₍ₓ₎=x²+2x+1+2*(x²-2x+x-2)+(x²-4x+4)
E₍ₓ₎= x²+2x+1+2(x²-x-2)+x²-4x+4
E₍ₓ₎=x²+2x+1+2x²-2x-4+x²-4x+4
E₍ₓ₎=4x²-4x+1= 2x²-2*2x*1+1²
E₍ₓ₎=(2x-1)² .......oricare ar fi x∈R
