Is it possible to make v the subject of this equation:

$\displaystyle

v^2 + \frac {2k v^2} {c^2} - \frac {k v^4} {c^4} = k

$

... where 'k' and 'c' are constants. Thanks, Ali Khan.

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- Sep 13th 2008, 04:30 AMAAKhan07Make 'v' the subject
Is it possible to make v the subject of this equation:

$\displaystyle

v^2 + \frac {2k v^2} {c^2} - \frac {k v^4} {c^4} = k

$

... where 'k' and 'c' are constants. Thanks, Ali Khan. - Sep 13th 2008, 04:35 AMmr fantastic
Yes.

First re-arrange:

$\displaystyle kv^4 - (2kc^2 + c^4) v^2 + kc^4 = 0$.

This is a quadratic equation in $\displaystyle v^2$ so use the quadratic formula to solve for $\displaystyle v^2$. The number of solutions will depend on the values of k and c.

Now solve for v. - Sep 13th 2008, 04:39 AMAAKhan07
Thanks, it's so obvious now that I think about it... in case you're interested, the calculation involves Quantum Theory, signals travelling back in time to collapse a wavefunction.