Răspuns:
E(n) = (n+1)² = patrat perfect
Explicație pas cu pas:
E(x) = (x²+x+1)²-(x²+x)²-x² =pp ?
E(x) = (x²+x+1)²-(x²+x)²-x²
Notam (x²+x+1) = a ; (x²+x) = b ;
E(x) = a²-b²-x² = (a-b)(a+b) - x²
E(x) = (x²+x+1-x²-x)(x²+x+1+x²+x) - x²
E(x) = 2x²+2x+1 - x² = x²+2x+1 = (x+1)²
E(x) = (x+1)² = patrat perfect
