Real Menace

Level pending

If\[a, b, c\]are distinct real numbers, find the number of real solutions to

\[\frac{(x-a)(x-b)}{(c-a)(c-b)}+\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+1=0\]

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