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 $100 \leq A \leq -100$ .

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