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tanvidais13

  • 3 years ago

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.

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  1. tanvidais13
    • 3 years ago
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    so do i need to expand the things using binomial, or what??

  2. tanvidais13
    • 3 years ago
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    because it's a mixture of AP's and GP's.

  3. mustry
    • 3 years ago
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    use binomial please if confused ask me please

  4. tanvidais13
    • 3 years ago
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    so i expanded it, but everything is in b's and c's and d's.

  5. slaaibak
    • 3 years ago
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    so use systems of equations.

  6. tanvidais13
    • 3 years ago
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    but then everything is equated to 0.

  7. tanvidais13
    • 3 years ago
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    does anyone have any idea as to what i could do here??

  8. mustry
    • 3 years ago
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    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

  9. slaaibak
    • 3 years ago
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    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.

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