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tanvidais13
Given that a + b(1+x)^3 + c(1+2x)^3 + d(1+3x)^3 = x^3, find the values for a, b c, d.
so do i need to expand the things using binomial, or what??
because it's a mixture of AP's and GP's.
use binomial please if confused ask me please
so i expanded it, but everything is in b's and c's and d's.
so use systems of equations.
but then everything is equated to 0.
does anyone have any idea as to what i could do here??
x^3+d (-1-9 x-27 x^2-27 x^3)+b (-1-3 x-3 x^2-x^3)-c(1+2 x)^3=a
a + b(1+x)^3 + c(1+2x)^3 + d(1+3x)^3 = x^3 a + b(1 + 3x + 3x^2 + x^3) + c(1 + 6x + 12x^2 + 8x^3) + d(1 + 9x + 27x^2 + 27x^3)=x^3 Now leave the RHS, and group the LHS accordingly: (b + 8c + 27c)x^3 + (3b + 12c + 27d)x^2 + (3b + 6c + 9c)x + (a + b + c + d) = x^3 it follows that: b + 8c + 27c=1 3b + 12c + 27d=0 3b + 6c + 9c=0 a + b + c + d =0 solve that.