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3 variables 3 equations (2 linear 1 quadratic) 
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#1
Jan2013, 12:10 PM

P: 40

1. The problem statement, all variables and given/known data
Find three numbers x,y,z satisfying the following equations: 9x6y10z=1 6x+4y+7z=0 x^{2}+y^{2}+z^{2}=9 2. Relevant equations 3. The attempt at a solution The book suggests that the best approach is to express 2 unknowns in terms of the third unknown from the first 2 linear equations and, by substituting these expressions in the last equation, obtain a quadratic equation for the third unknown. So i try this: 4(9x6y10z=1)= 36x24y40z=4 6(6x+4y+7z=0)= 36x+24y+42z=0 (36x24y40z=4) + (36x+24y+42z=0)= 2z=4 z=2 I figure I've gone wrong somewhere because this is not the strategy outlined in the book (it's also not the correct answer for z according to the book) 


#2
Jan2013, 12:32 PM

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#3
Jan2013, 01:01 PM

P: 40

Thanks for your reply. On further inspection I realise that the book does in fact say that z is equal to 2. However this still leaves me a bit confused about the purpose of the quadratic equation since it seems it is superfluous to the requirements for providing a solution.
The problem is question 1A, page 44 (in the pdf digital copy. Or 22 in the hard copy) of this book: http://www.scribd.com/doc/39412845/M...icsPolya1954 


#4
Jan2013, 01:08 PM

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P: 4,958

3 variables 3 equations (2 linear 1 quadratic)



#5
Jan2013, 03:30 PM

P: 40

Thanks for the help I'll try that.



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