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Thread: By using algebraic method, find the value of the smallest value

  1. #1
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    By using algebraic method, find the value of the smallest value

    Question:
    The subtraction of two positive numbers is $\displaystyle 4$. When the two numbers are multiplied together, the resulting value is $\displaystyle 21$. By using algebraic method, find the value of the smallest number

    My workings:
    let $\displaystyle x$ be the smallest number
    let $\displaystyle x+4$ be the bigger number
    $\displaystyle (x+4)-x=4$
    $\displaystyle (x+4)$ x$\displaystyle x=21$
    $\displaystyle x+4=4+x$
    $\displaystyle (x^2+4x)/4 = 21/4$
    $\displaystyle 4(x^2+4x)=84$
    $\displaystyle 4x^2+16x=84$
    $\displaystyle 4x^2+16x-84=0$
    $\displaystyle (x+7)$ or $\displaystyle (4x-12)$
    $\displaystyle x+7=0$ or $\displaystyle 4x-12=0$
    $\displaystyle x=-7$ (N.A.) or $\displaystyle 4x-12=0$
    Therefore, $\displaystyle x=3$

    Am I right?

    Thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: By using algebraic method, find the value of the smallest value

    Quote Originally Posted by FailInMaths View Post
    Question:
    The subtraction of two positive numbers is $\displaystyle 4$. When the two numbers are multiplied together, the resulting value is $\displaystyle 21$. By using algebraic method, find the value of the smallest number

    My workings:
    let $\displaystyle x$ be the smallest number
    let $\displaystyle x+4$ be the bigger number
    $\displaystyle (x+4)-x=4$
    $\displaystyle (x+4)$ x$\displaystyle x=21$
    $\displaystyle x+4=4+x$
    $\displaystyle (x^2+4x)/4 = 21/4$
    $\displaystyle 4(x^2+4x)=84$
    $\displaystyle 4x^2+16x=84$
    $\displaystyle 4x^2+16x-84=0$
    $\displaystyle (x+7)$ or $\displaystyle (4x-12)$
    $\displaystyle x+7=0$ or $\displaystyle 4x-12=0$
    $\displaystyle x=-7$ (N.A.) or $\displaystyle 4x-12=0$
    Therefore, $\displaystyle x=3$

    Am I right?

    Thanks
    Plug your numbers into the original equations and see if it works.
    Given that your smaller number is 3 then your larger number is 7.

    $\displaystyle 7 - 3 = 4 \text{ and } 7 \times 3 = 21$

    Since that is true and matches the question statement your answer is correct.


    Your working confused me though, why didn't you just go from saying $\displaystyle x(x+4) = 21$ in the second line to $\displaystyle x^2+4x = 21$ and then $\displaystyle x^2+4x-21=0$ and solve that quadratic?
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  3. #3
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    Re: By using algebraic method, find the value of the smallest value

    Quote Originally Posted by e^(i*pi) View Post
    Plug your numbers into the original equations and see if it works.
    Given that your smaller number is 3 then your larger number is 7.

    $\displaystyle 7 - 3 = 4 \text{ and } 7 \times 3 = 21$

    Since that is true and matches the question statement your answer is correct.


    Your working confused me though, why didn't you just go from saying $\displaystyle x(x+4) = 21$ in the second line to $\displaystyle x^2+4x = 21$ and then $\displaystyle x^2+4x-21=0$ and solve that quadratic?
    Oh, now that you say it. To be honest, I had been thinking for a few hours, so I am not really sure of what I am writing, thus want to have it checked here

    Thanks for spotting the mistake, I will amend it.

    Thanks
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