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Math Help - Quadratic Equation

  1. #1
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    Quadratic Equation

    can someone help me on this?
    solve the quadratic equations by factoring

    (x + 2)^3 = x^3 + 8
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  2. #2
    TD!
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    If you know 8 = 2, you see a sum of squares.

    <br />
x^3  + 2^3  = \left( {x + 2} \right)\left( {x^2  - 2x + 4} \right)<br />

    Everything to the left, factor (x+2) and simplify:

    <br />
\begin{array}{l}<br />
 \left( {x + 2} \right)^3  - \left( {x + 2} \right)\left( {x^2  - 2x + 4} \right) = 0 \\ \\<br />
 \left( {x + 2} \right)\left( {\left( {x + 2} \right)^2  - \left( {x^2  - 2x + 4} \right)} \right) = 0 \\ \\<br />
 \left( {x + 2} \right)\left( {6x} \right) = 0 \Leftrightarrow x =  - 2 \vee x = 0 \\ <br />
 \end{array}<br />
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  3. #3
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    Quote Originally Posted by danielwu
    can someone help me on this?
    solve the quadratic equations by factoring

    (x + 2)^3 = x^3 + 8
    Or, less elegantly:
    (x+2)^3 = x^3 + 3 \cdot 2x^2 + 3 \cdot 2^2x + 2^3 = x^3 + 6x^2 + 12x + 8

    So
    x^3 + 6x^2 + 12x + 8 = x^3 + 8

    6x^2 + 12 x = 0

    (6x)(x+2) = 0

    etc.

    -Dan
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