Explaining a rejected root and a false surd rule

Do not use a calculator in this question.

1. Amir solves \(\sqrt{2x+7}=x-4\). He squares both sides, obtains \(x^2-10x+9=0\) and gives two answers, \(x=1\) and \(x=9\). Explain why one of his answers must be rejected, and state the solution of the equation.
2. Bea claims that \(\sqrt{x+9}=\sqrt{x}+3\) for every \(x\ge0\). Show that her claim is false, and find the only value of \(x\) for which it is true.