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Math Help - Completing the square.

  1. #1
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    Completing the square.

    Hi can someone please help me with this:

    In a triangle, ABC, AB=(2-x)cm, BC=(x+1)cm and angle ABC=120;

    a) show that AC^2 = x^2 - x + 7 - i did this using the cosine rule.

    b) Find the value of x for which AC has a minimum value: (I need to complete the square to find x)

    I get this far;

    (x - \frac{1}{2})^2 - (-\frac{1}{2})^2 + 7

    (x - \frac{1}{2})^2 = - \frac{27}{4}^2

    Can you show me in stages how to resolve to find a minimum value for x?

    Thanks,

    F.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Flexible View Post
    Hi can someone please help me with this:

    In a triangle, ABC, AB=(2-x)cm, BC=(x+1)cm and angle ABC=120;

    a) show that AC^2 = x^2 - x + 7 - i did this using the cosine rule.

    b) Find the value of x for which AC has a minimum value: (I need to complete the square to find x)

    I get this far;

    (x - \frac{1}{2})^2 - (-\frac{1}{2})^2 + 7{\color{red}=0}

    (x - \frac{1}{2})^2 = - \frac{27}{4} I took the exponent off your right hand side to make it correct.

    Can you show me in stages how to resolve to find a minimum value for x?

    Thanks,

    F.
    You don't have to complete the square to find the min value.

    Just use x=-\frac{b}{2a} in ax^2+bx+c=0

    This will give you the x-coordinate of the vertex of your parabola.

    x^2-x+7=0

    \frac{-(-1)}{2(1)}=\frac{1}{2}

    Now, find f\left(\frac{1}{2}\right) and that will be your min value.
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  3. #3
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    i found this video helpful on completing the square

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