# Is this really a linear equation?

1. Sep 15, 2011

### chris_0101

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

Thanks

2. Sep 15, 2011

### daveb

I'm guessing the book is wrong in this instance. Linear equations have all variables with constant coefficients and variables to the 1st power.

3. Sep 15, 2011

### QuarkCharmer

Do x sub 1, 2, and 3 represent anything? Or did you mean to give them exponents?

4. Sep 15, 2011

### chris_0101

I copied it straight from the text. x sub 1, 2 and 3 I assume are the 3 different x parameters

5. Sep 15, 2011

### Staff: Mentor

I agree with daveb. The equation is not a linear equation.

6. Sep 15, 2011

### HallsofIvy

Staff Emeritus
What is the exact wording of the question? This equation is linear "in $x_1$ and $x_2$". It is NOT linear "in $x_3$" or "in $x_1$, $x_2$, and $x_3$"

7. Sep 15, 2011

### chris_0101

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

8. Sep 15, 2011

### dynamicsolo

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.")

9. Sep 16, 2011

### 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?

10. Sep 16, 2011

### Hootenanny

Staff Emeritus
Using indices, or indexed variables such as $x_i$, is a standard notation in mathematics.