Răspuns:
Explicație pas cu pas:
E(x) = (x+1)²+2(x+1)(x-2) +(x-2)²
Daca notam x+1 = a ; x-2 = b =>
E(x) = a²+2ab+b² = (a+b)² =>
Inlocuim a si b =>
E(x) = (x+1+x-2)² = (2x-1)²
b) E(√2)+a√2 ∈ N ; a = ? ; a ∈N
E(√2) = (2·√2-1)² = (2√2)²-2·2√2·1+1² = 8-4√2+1 = 9-4√2
E(√2)+a√2 = 9-4√2 + a√2
E(√2)+a√2 ∈ N => E(√2)+a√2 = 9-4√2 + 4√2 = 9 =>
a = 4
