It's more fun in Cubic Equation

Algebra Level 5

Let \(r,s\) and \(t\) be the roots of \(x^3+ x\sqrt{A} + x\sqrt{2A} + A =0\). Find \[ \frac{(r+s+t)(r+s-t)}{r^2+s^2-t^2+2rs}\] where \( 100 \leq A \leq -100\).

Image Credit: Wikimedia Francois Viete
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