Bonjour
solution postée
voici la solution de mt2sr
P(x)=a_nx^n+...+a_0
on pour tout a>0 a+1/a>=2
P(x)*P(1/x)=sum(a_i, 0<=i<=n)+sum(a_i*a_j*x^(i-j), 0<=i<j<=n)+sum(a_i*a_j*x^(i-j), 0<=j<i<=n)
=sum(a_i, 0<=i<=n)+sum(a_i*a_j*(x^(i-j)+x^(j-i)), 0<=j<i<=n)
>=sum(a_i, 0<=i<=n)+2sum(a_i*a_j), 0<=j<i<=n)
=P(1)*P(1/1)>1