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How is the equation $x_1+5x_2-\sqrt{(2x_3)} = 1$ a linear equation? The answer given in the book is, "The Equation is linear".

How can an equation involving a square root like the above equation be a linear equation?

here is the cutting of the book, enter image description here

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    Shouldn't they have written it as $x_3\sqrt2$ to avoid this mess in the first place?2012-12-26

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Answer to title question: It's NOT!

Your question is legitimate:

$x_1+5x_2-\sqrt{2x_3\;} = 1\tag{1}$

$(1)$ is not a linear equation as you suggest.

Nor is $(f)$ linear, as typeset in the image.


I suspect there was a misprint in the problem set (book), or a careless typo that the author (and/or editor) over-looked, and which was intended to be:

$x_1 + 5x_2 - \sqrt{2}\;\cdot x_3 = 1\tag{2}$

NOW, $(2)$ is a linear equation.

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    No problem, Zia ur. I would have been perplexed too, had I encountered that question as written in the older edition!2012-12-26
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Here is the real exercise found on Amazon...

enter image description here

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    This picture is from the latest edition. It seems in some earlier edition the erroneous statements appear (see the question itself). Nowadays textbooks have on-line errata sites. In the olden days it was not so easy...2012-12-26
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$(x+5y-1)=\sqrt{2z}$ so $(x+5y-1)^2=2z$ and this is not a linear equation because the order of variabes are 2.

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    @amWhy: thanks so much. $\ddot\smile$2013-02-07