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tmua.me Tau Paper 2 · Q19

Paper 2AlgebraLogic & proof

A set SS consists of six distinct real numbers. For every r∈Sr\in S, suppose that

∑s∈Ss≠r1r−s=r3.\sum_{\substack{s\in S\\s\ne r}}\frac1{r-s}=r^3.

What is the value of ∑r∈Sr2\displaystyle\sum_{r\in S}r^2?

A45+125\sqrt{45+12\sqrt5}
B30−125\sqrt{30-12\sqrt5}
C15+65\sqrt{15+6\sqrt5}
D30+65\sqrt{30+6\sqrt5}
E30+125\sqrt{30+12\sqrt5}

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