# Thread: no. of roots pf a equation.

1. ## no. of roots pf a equation.

my textbook says that that no. of solutions to the equation x+y+z=c is given by
the co efficient of x^c in the expansion of {(1+x^2+x^3+...........+x^c)}^3.
but the mechanism is not mentioned here.
i have been able to get that it is just the no. of triplets of digits of nos. less than c that give a sum of c.but how do they connect this concept to the binomial expansion given above.

2. ## Re: no. of roots pf a equation.

This is pretty similar to what I wrote in another thread:
Originally Posted by emakarov
Indeed, to get $x^r$ one needs to choose some $x^i$ from the first factor, $x^j$ from the second factor and $x^k$ from the third factor so that $i+j+k=r$. The number of such choices equals the coefficient of $x^r$.
Does this make sense?