# 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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