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Removing sqr from binomial

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Mikebits

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So say we have x²-2. Is there a way to rid the square and keep the binomial true? In other words we need to keep it X+/-? in the for x+? or x-? but do away with the square.
 
So say we have x²-2. Is there a way to rid the square and keep the binomial true? In other words we need to keep it X+/-? in the for x+? or x-? but do away with the square.

i remember "modulus" represented by two vertical lines one on each side, -- if I am right, it might mean positive value of the parameter?

Modulus function

never practiced for last 40 years, thus no continuity
 
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So say we have x²-2. Is there a way to rid the square and keep the binomial true? In other words we need to keep it X+/-? in the for x+? or x-? but do away with the square.

Are you asking how x²-2 can be factored? if that's the case, x²-2 = (x+√2)(x-√2)
 
If you can accept an approximation, you can linearize about a selected point.
Use a Taylor Series Expansion, but take only the first two terms .....
Taylor series - Wikipedia, the free encyclopedia
..... If your independent variable value is too far removed from the evaluation point, the approximation won't be valid. ... Just depends on what your objective is.
 
My objective was to solve a polynomial long division problem using synthetic division, because I screw up long division. So Say I have

x²-2/8x²-x-2

This would have to be done with long division, but if it were in the form
x-?/8x²-x-2

It could be done with synthetic division.
 
My objective was to solve a polynomial long division problem using synthetic division, because I screw up long division. So Say I have

x²-2/8x²-x-2

This would have to be done with long division, but if it were in the form
x-?/8x²-x-2

It could be done with synthetic division.

Solved by my wife:
1/8 + (1/8)(x-14)/(8x²-x-2)

No warranty implied ;)
 
Your right Sarma. I got the numerator denominator swapped. :eek:

if (x²-2)/(8x²-x-2) is the correct, I already posted an equivalent expression in which the numerator is a 1st-degree binomial. Have you checked it??

if the numerator and the denominator are swapped :confused: it's even simpler to get rid of the square with simple algebra.
 
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