Now how do I do this?

Geometry Level 4

Let area of the triangle formed by the points \((b,c)\), \((c,a)\) and \((a,b)\) as vertices be \(\Delta\) and the area of the triangle whose veritces are \((ac-b^2,ab-c^2)\), \((ba-c^2,bc-a^2)\) and \((cb-a^2,ca-b^2)\) be \(\Delta_1\). Also define \(z\) as \[z = \begin{vmatrix} a&b&c \\ b&c&a \\ c&a&b \end{vmatrix}\] Find the value of \[\sqrt{z^2\cdot \dfrac{\Delta}{\Delta_1}}\]

Details: Take \(a=3\), \(b=5\), \(c=8\).

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