Exercise 19, § 8

Let K be a Henselian field with a valuation v. Let E be a finite-dimensional vector space over K and Q a non-degenerate quadratic form on E such that the relation $Q(x) = 0$ implies $x = 0$. Let

be the associated bilinear form. Show that $2v(\Phi(x, y)) \geq v(Q(x)) + v(Q(y))$; deduce that