- #1
Miike012
- 1,009
- 0
how do you find the perfect square of say
ax2 + b/x2 + c
??
ax2 + b/x2 + c
??
How Can an Expression Like ax^2 + b/x^2 + c Be a Perfect Square?
- Thread starter Miike012
- Start date
-
- Tags
- Square
In summary: 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{
- #2
Mentallic
Homework Helper
- 3,802
- 95
You can't find the perfect square of that problem precisely, unless you're satisfied with [tex]\left(\sqrt{ax^2+\frac{b}{x^2}+c}\right)^2[/tex] which I doubt since it's trivial, but take a look at the expansion of
[tex]\left(x+\frac{1}{x}\right)^2[/tex]
[tex]\left(x+\frac{1}{x}\right)^2[/tex]
- #3
Mark44
Mentor
- 37,782
- 10,170
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.Miike012 said:
- #4
Mentallic
Homework Helper
- 3,802
- 95
Mark44 said:
That possibility completely skipped my mind
- #5
Mark44
Mentor
- 37,782
- 10,170
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.
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
Miike012
- 1,009
- 0
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 ?
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 ?
Attachments
- #7
Mentallic
Homework Helper
- 3,802
- 95
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.Mark44 said:
When you get to the expression
[tex]\frac{25}{36}x^8+\frac{1}{2}+\frac{9}{100}x^{-8}[/tex]
You should realize that it could be of the form [tex]\left(ax^4+bx^{-4}\right)^2[/tex] where in this case [tex]a=\sqrt{\frac{25}{36}}=\frac{5}{6}[/tex]
[tex]b=\sqrt{\frac{9}{100}}=\frac{3}{10}[/tex]
And all you'd need to do is check to see if [tex]2\cdot \frac{5}{6}\cdot \frac{3}{10} =\frac{1}{2}[/tex]
FAQ: How Can an Expression Like ax^2 + b/x^2 + c Be a Perfect Square?
What is a perfect square?
A perfect square is a number that is the result of multiplying a whole number by itself. For example, 4 is a perfect square because it is the result of multiplying 2 by 2 (2 x 2 = 4).
How do you find the perfect square of a number?
To find the perfect square of a number, you can take the square root of the number. The square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 x 3 = 9.
What is the difference between a perfect square and a square number?
A perfect square is a number that is the result of multiplying a whole number by itself, while a square number is any number that can be represented as the product of two equal integers. For example, 9 is a perfect square (3 x 3 = 9) and also a square number (9 = 3 x 3).
Can negative numbers be perfect squares?
No, negative numbers cannot be perfect squares. This is because a perfect square is always a positive number, since multiplying a negative number by itself would result in a positive number.
How can finding perfect squares be useful in real life?
Finding perfect squares can be useful in many situations, such as calculating the area of a square-shaped object or determining the length of a side in a geometric shape. It can also be helpful in solving algebraic equations and in understanding patterns in mathematics.