Răspuns:
E(x)=(x+2)²-2(x+3)-5=
x²+4x+4-2x-6-5=
x²+2x-7
0<E(n)≤11
0<n²+2n-7≤11
observi ca pt n=2 E(2)=2²+2·2-7=4+4-7=1>0
n²+2n-7=11
n²+2n-7-11=0
n²+2n-11=0
Δ=2²-4·(-11)=4+44=48
n1=(2-√48)/2=(2-√16*3)/2=
(2-4√3)/2=1-2√3<3
n2=1+2√3≠1+2·1,8≈1+3,6≈4,6=>
n=4
Explicație pas cu pas:
