Given that \(\dfrac8{3-\sqrt5}=\sqrt{a+b\sqrt5}\), where \(a\) and \(b\) are integers, find, without using a calculator, the value of \(a\) and of \(b\).[4]
Given that \(4-\sqrt7\) is a root of the equation \(-x^2+px+q=0\), where \(p\) and \(q\) are integers, find the value of \(p\) and of \(q\).[4]
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