Răspuns:
Explicație pas cu pas:
E(x) = (x + 3)² – (x + 1)² – (x + 3)(x – 3) + (x + 1)(x – 1)
E(x) = (x+3+x+1)(x+3-x-1) + x²-9 + x²-1
E(x) = (2x+4)·2 + 2x²-10
E(x) = 4x+8 -10+2x²
E(x) = 2x²+4x-2
E(x) = 2(x²+2x-1)
E(n) = 20 =>
2n²+4n-2 = 20 =>
2n²+4n-22 = 0 =>
n²+2n-11 = 0
n²+2n = 11 <=>
n(n+2) = 11 =>
nu exista numere naturale care indeplinesc conditia data
n²+2n-11 = 0 =>
n₁,₂ = [-2±√(4+44)] / 2
n₁,₂ = (-2±4√3)/2 = -1±2√3
