Finding the perfect square

1. Mar 10, 2012

Miike012

how do you find the perfect square of say

ax2 + b/x2 + c
??

2. Mar 10, 2012

Mentallic

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

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

3. Mar 11, 2012

Staff: Mentor

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.

4. Mar 11, 2012

Mentallic

That possibility completely skipped my mind

5. Mar 11, 2012

Staff: 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.

6. Mar 11, 2012

Miike012

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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7. Mar 11, 2012

Mentallic

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 $$2\cdot \frac{5}{6}\cdot \frac{3}{10} =\frac{1}{2}$$