The lengths of the diagonals \(PR\) and \(QS\) of the rhombus \(PQRS\) are \((4+2\sqrt3)\text{ cm}\) and \(\left(\dfrac6{2+\sqrt3}\right)\text{ cm}\) respectively. Find the value of \(PQ^2\), leaving your answer in the form \(a+b\sqrt c\).[4]
Determine if the curve \(y=px^2+8x+p-6\) lies completely above or below the \(x\)-axis for \(p>8\).[3]
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Answer:(a) \(PQ^2=70-32\sqrt3\text{ cm}^2\); (b) completely above the \(x\)-axis.