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Math Help - no. of roots pf a equation.

  1. #1
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    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.
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  2. #2
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    Re: no. of roots pf a equation.

    This is pretty similar to what I wrote in another thread:
    Quote Originally Posted by emakarov View Post
    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?
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