There is a theorem that n powered equation have n roots.
But this equation:
root over x or x^1/2=4 should have 1/2 roots but it have one root , 16.
another example is,
x^3/2=2^3/2 should have 3/2 roots but it has one root, 2
It creates problem if we factorise this equation like this:
x^3-8=0 into [x^3/2-2^3/2][x^3/2+2^3/2]=0
But it gives two roots,2and -2 while -2 is not the real root.
Why is this happened?
Fractional index
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Re: Fractional index
code of $\sqrt{x}$ is \sqrt{x} ... just put two dollar sign in both side of it...
code of $x^2$ is x^2...
you can also see the code by double clicking on a LaTeXed equation...
writing without LaTeX looks like a mess and many wouldn't like to read 'em...
code of $x^2$ is x^2...
you can also see the code by double clicking on a LaTeXed equation...
writing without LaTeX looks like a mess and many wouldn't like to read 'em...
Re: Fractional index
Polynomials of degree $n$ have $n$ roots. Polynomials have only nonnegative integer powers of the variable. If you have fractional powers than it's not a polynomial anymore.
For your second question, $(-2)^{3/2}$ is not a real number. So, $-2$ is not a solution even after you factorize it. You have to be careful when you take fractional power.
For your second question, $(-2)^{3/2}$ is not a real number. So, $-2$ is not a solution even after you factorize it. You have to be careful when you take fractional power.