# Finding the perfect square

how do you find the perfect square of say

ax2 + b/x2 + c
??

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Mentallic
Homework Helper
You can't find the perfect square of that problem precisely, unless you're satisfied with $$\left(\sqrt{ax^2+\frac{b}{x^2}+c}\right)^2$$ which I doubt since it's trivial, but take a look at the expansion of

$$\left(x+\frac{1}{x}\right)^2$$

Mark44
Mentor
how do you find the perfect square of say

ax2 + b/x2 + c
??
You didn't by chance mean (ax2 + b)/(x2 + c), did you? If so, the lack of parentheses around the numerator and denominator completely confused Mentallic about what you're asking.

Mentallic
Homework Helper
You didn't by chance mean (ax2 + b)/(x2 + c), did you? If so, the lack of parentheses around the numerator and denominator completely confused Mentallic about what you're asking.
That possibility completely skipped my mind Mark44
Mentor
Mentallic,
Well, I'm about as puzzled by this problem as you must be. The way I read it, the OP just wants to square the original expression, whatever it is.

Nope that is what I ment to say.. I added an example to the paint doc and highlighted the portion in red.

It has to do with finding the surface area of a curve... and basically I was unaware the equation could be turned into a perfect square... so was wondering if there is some pattern I should look for ?

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Mentallic
Homework Helper
Mentallic,
Well, I'm about as puzzled by this problem as you must be. The way I read it, the OP just wants to square the original expression, whatever it is.
I didn't have any doubts about what the OP is trying to do, just what the expression was meant to be once you raised the point.

Mike, like I was saying it doesn't work in general that ax2 + b/x2 + c can be turned into a perfect square, but in this case c happened to be the right number for the job.

When you get to the expression

$$\frac{25}{36}x^8+\frac{1}{2}+\frac{9}{100}x^{-8}$$

You should realize that it could be of the form $$\left(ax^4+bx^{-4}\right)^2$$ where in this case $$a=\sqrt{\frac{25}{36}}=\frac{5}{6}$$
$$b=\sqrt{\frac{9}{100}}=\frac{3}{10}$$

And all you'd need to do is check to see if $$2\cdot \frac{5}{6}\cdot \frac{3}{10} =\frac{1}{2}$$