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Homework Help: Is this really a linear equation?

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data
    The question is asking whether or not the given equations are linear. I am unsure whether this equation (below) is linear or not?

    x1 + 5x2 - sqrt(2x3) = 1

    3. The attempt at a solution

    My initial answer is that it is not due to the fact that a linear equation does not contain any roots (mentioned in the textbook itself), however, the textbook answers show that the given equation is in fact a linear equation. Why is this possible?

    Any help is greatly appreciated

  2. jcsd
  3. Sep 15, 2011 #2
    I'm guessing the book is wrong in this instance. Linear equations have all variables with constant coefficients and variables to the 1st power.
  4. Sep 15, 2011 #3
    Do x sub 1, 2, and 3 represent anything? Or did you mean to give them exponents?
  5. Sep 15, 2011 #4
    I copied it straight from the text. x sub 1, 2 and 3 I assume are the 3 different x parameters
  6. Sep 15, 2011 #5


    Staff: Mentor

    I agree with daveb. The equation is not a linear equation.
  7. Sep 15, 2011 #6


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    Science Advisor

    What is the exact wording of the question? This equation is linear "in [itex]x_1[/itex] and [itex]x_2[/itex]". It is NOT linear "in [itex]x_3[/itex]" or "in [itex]x_1[/itex], [itex]x_2[/itex], and [itex]x_3[/itex]"
  8. Sep 15, 2011 #7
    I'll write it out again:

    1) In each part, determine whether the equation is linear in x_1,x_2,x_3

    a) x_1 + 5x_2 - sqrt(2x_3) = 1

    the answer at the back of the book: Equation a) is a linear equation
  9. Sep 15, 2011 #8


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    Homework Helper

    The answer is wrong for the reason given by my colleagues above...

    It would be interesting to know if the problem had been revised from a previous edition of the book; I've seen many cases of a problem being changed in a new edition without the author/editors going back and revising the answer. (My favorite was a physics text in which the question portion required a numerical answer, and the answer given in the back of the book was "Yes.")
  10. Sep 16, 2011 #9


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    Staff: Mentor

    What are some of the other questions in this chapter? Do they all use this peculiar x_1 notation? Have you encountered this notation in any other questions in that textbook?
  11. Sep 16, 2011 #10


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    Staff Emeritus
    Science Advisor
    Gold Member

    Using indices, or indexed variables such as [itex]x_i[/itex], is a standard notation in mathematics.
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