We choose $I = [-1,1]$ and fix any very good extremal pair $(Q, R)$. We set $P = QR$ and denote by $x_1 \leq \ldots \leq x_{n+m}$ the roots of $P$ counted with multiplicity. Following the method used in question 4.39, show that there exists an element $y \in ]x_m, x_{m+1}[$ such that $|P(y)| = \|P\|_I$.