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Math Help - Maximum values

  1. #1
    Newbie Tom G's Avatar
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    Maximum values

    in triangle PQR, PQ=(x+2)cm, PR=(5-x)cm and <QPR=30. the area(A) of the trangle is 1/4(10+3x-x^2)

    the question i am struggling with is this; "use the method of completing the square to find the maximum value of A and the corresponding value of x."

    i'd be grateful for someone to explain how its done and to also say what is done if it is a minimum value in case that another question asks me to find the minimum. thanks MHF.
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by Tom G View Post
    in triangle PQR, PQ=(x+2)cm, PR=(5-x)cm and <QPR=30. the area(A) of the trangle is 1/4(10+3x-x^2)

    the question i am struggling with is this; "use the method of completing the square to find the maximum value of A and the corresponding value of x."

    i'd be grateful for someone to explain how its done and to also say what is done if it is a minimum value in case that another question asks me to find the minimum. thanks MHF.
    \frac14(10+3x-x^2)

    \Rightarrow\frac14(\frac94 + 10 - \frac94 + 2\frac32 x-x^2)

    \Rightarrow\frac14(\frac94 + 10 - (x - \frac32)^2)

    So you are subtracting from some number, when will it be maximum??
    Ans: If you subtract minimum value. minimum of (x - \frac32)^2 is 0 and that is when x=\frac32

    So maximum value of Area is \frac{49}{16}
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  3. #3
    Member Glaysher's Avatar
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    Quote Originally Posted by Tom G View Post
    in triangle PQR, PQ=(x+2)cm, PR=(5-x)cm and <QPR=30. the area(A) of the trangle is 1/4(10+3x-x^2)

    the question i am struggling with is this; "use the method of completing the square to find the maximum value of A and the corresponding value of x."

    i'd be grateful for someone to explain how its done and to also say what is done if it is a minimum value in case that another question asks me to find the minimum. thanks MHF.
    If you go back to C1 notes you will find that:

    a(x-b)^2+c
    a>0

    has minimum value c at x=b

    and

    -a(x-b)^2+c
    a>0

    has maximum value c at x=b
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