3 [A polynomial of degree $\mathrm{n}$ has no more than $\mathrm{n}$ roots]

Solve the equation $c \frac{(x-a)(x-b)}{(c-a)(c-b)}+b \frac{(x-a)(x-c)}{(b-a)(b-c)}+a \frac{(x-b)(x-c)}{(a-b)(a-c)}=x$.
On the left, there is a polynomial of degree no higher than 2. But the equation has at least 3 roots $-a, b$ and $c$ (these numbers are distinct, otherwise the equation makes no sense). Therefore, the difference between the left and right sides is identically zero.

## Answer

$x-$ any number.

Problem