It's more fun in Cubic Equation

Algebra Level 5

Let r,sr,s and tt be the roots of x3+xA+x2A+A=0x^3+ x\sqrt{A} + x\sqrt{2A} + A =0. Find (r+s+t)(r+st)r2+s2t2+2rs \frac{(r+s+t)(r+s-t)}{r^2+s^2-t^2+2rs} where 100A100 100 \leq A \leq -100.

Image Credit: Wikimedia Francois Viete
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