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Math Help - Simple equations

  1. #1
    Senior Member Mukilab's Avatar
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    Simple equations

    Hi could someone point out to me the steps for solving this equation. I've got so far...












    I need to make a poster about vedic maths and I can solve this within seconds with vedic maths but I'm stuck with the traditional method. Any help?
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  2. #2
    Super Member Bacterius's Avatar
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    \frac{6x + 13}{3x + 7} = \frac{9x + 4}{12x + 10}

    Put under common denominator.

    \frac{(6x + 13)(12x + 10)}{(3x + 7)(12x + 10)} = \frac{(9x + 4)(3x + 7)}{(12x + 10)(3x + 7)}

    Simplify (get rid of fractions) :

    (6x + 13)(12x + 10) = (9x + 4)(3x + 7)

    Expand :

    72x^2 + 60x + 156x + 130 = 27x^2 + 63x + 12x + 28

    Simplify :

    72x^2 + 216x + 130 = 27x^2 + 75x + 28

    Make the right-hand side 0 :

    45x^2 + 141x + 102 = 0

    Use the quadratic formula and you are done :

    \triangle = b^2 - 4ac = 141^2 - 4 \times 45 \times 102 = 1521

    Solutions :

    x_1 = \frac{-b - \sqrt{\triangle}}{2a} = \frac{-141 - 39}{90} = \frac{-180}{90} = -2

    x_2 = \frac{-b + \sqrt{\triangle}}{2a} = \frac{-141 + 39}{90} = \frac{-102}{90} = \frac{-17}{15}

    Solutions are -2 and \frac{-17}{15}
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  3. #3
    Senior Member Mukilab's Avatar
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    Thanks but I need to explain it to a simple audience, ages of 11-13. I would rather not use the quadratic formula, thanks for contributing though.
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  4. #4
    Super Member Bacterius's Avatar
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    Ah, right. But the problem is, coefficients of your equation are quite impressive, why not take smaller numbers so as to get a smaller quadratic equation, easy to understand and factorize mentally (without quadratic formula) for those young people ? Something like x^2 + 10x - 25 ? You know, the product and sum of roots : 25 = 5 \times 5, but 10 = 5 + 5, thus x^2 + 10x - 25 = (x - 5)(x + 5)
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  5. #5
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by Bacterius View Post
    Ah, right. But the problem is, coefficients of your equation are quite impressive, why not take smaller numbers so as to get a smaller quadratic equation, easy to understand and factorize mentally (without quadratic formula) for those young people ? Something like x^2 + 10x - 25 ? You know, the product and sum of roots : 25 = 5 \times 5, but 10 = 5 + 5, thus x^2 + 10x - 25 = (x - 5)(x + 5)

    Well the actual point I am trying to make is that these people learn a little of vedic maths or are interested in it.

    For example.


    In my head, within 3 seconds I can instantly work out that 15x=-17 so x=\frac{-17}{15} and 3x+6=0 so x=-2
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  6. #6
    Super Member Bacterius's Avatar
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    Oh I see, didn't get "vedic". Well I don't really know this kind of mental mathematics, so I think I won't be able to help you further
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  7. #7
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by Bacterius View Post
    Oh I see, didn't get "vedic". Well I don't really know this kind of mental mathematics, so I think I won't be able to help you further
    well, do you know any simple equations along those lines but with the x^2 canceling out?


    I might have to rewrite my whole poster D; or just leave it at that...
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  8. #8
    Senior Member Mukilab's Avatar
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    Test for poster:

    6x+13+9x+4\longrightarrow15x+17

    3x+7+12x+10\longrightarrow15x+17

    x=\frac{-17}{15}

    (6x+13)-(3x+7)=3x+6

    (12x+10)-(9x+4)=3x+6

    x=\frac{-6}{3}=-2
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  9. #9
    Senior Member Mukilab's Avatar
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    Can't upload a file (it's a .pub which isn't allowed). So here's a screenie. Sorry for all the boxes and dotted lines. None of that will be there when printed.

    I got the Vedic Maths logo from google after changing it a bit.

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  10. #10
    Super Member Bacterius's Avatar
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    Did you check copyright for the logo though ? One of the kids might sue you
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  11. #11
    Senior Member Mukilab's Avatar
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    :P


    Not copyright *thank god*
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  12. #12
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    Smile @Mukilab

    Hi Mukilab!

    Just saw ur questions on Quadratics.
    You are right these can be solved in few seconds with Vedic Math.
    Its easy.

    I liked ur Poster.When you r through why dont u send it to me ...If you would like I can put it up on our vedic Maths Blog.

    Feel free to mail me if you need any more help with regards to Vedic Maths.


    Thanks

    Warm Wishes
    Gaurav

    Gaurav Tekriwal
    President
    The Vedic Math Forum India
    www.vedicmathsindia.org
    Follow us on Twitter: gtekriwal (VedicMathsIndia) on Twitter
    We Blog Actively at : Vedic Maths Forum India Blog
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  13. #13
    Senior Member Mukilab's Avatar
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    Hello gtekriwal, nice to see it's your first post, and although I am quite a new member, Welcome!

    No problem, although I hope you don't mind my caution. I'll hand it in to my maths teacher before I email it to you. Is it OK if I mention this blog to them?

    Oh and I'll definitely be hoping to study all the sutras, I only know about half. Hopefully in time my knowledge will gradually expand and I'll learn these much simpler methods. Unfortunately, knowledge comes hand in hand with practice which I have learned in studying vertically by crosswise. It gets fairly confusing with the three digits in your head.

    Nice forum by the way! Hope it prospers


    ~Muki
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  14. #14
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    Hi Muki,

    Thanks for ur warm welcome.

    U can please share the blog and the website with your teachers. No Issues.


    Where r u from? Are u from India?

    Do keep in touch.

    Cheers
    Gaurav
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  15. #15
    Senior Member Mukilab's Avatar
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    England in fact, I actually did this as a GnT course (Gifted 'n' Talented) with several other pupils. We had several lessons regarding this and other areas of mathematics and we were asked to create a poster on one or more sutras from vedic maths. I found it a very enjoyable experience!
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