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- Feb 14, 2012
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If $\log_4 (a+2b)+\log_4 (a-2b)=1$, find the minimum of $|a|-|b|$.
If $\log_4 (a+2b)+\log_4 (a-2b)=1$, find the minimum of $|a|-|b|$.
Thanks for participating, chisigma! I noticed you stopped half-way and probably you could eyeball the answer from where you have stopped?From the initial conditions we derive immediately...
$\displaystyle (a + 2\ b)\ (a - 2\ b) = 4 -> b = \frac{\sqrt{a^{2} - 4}}{2}\ (1)$
... so that the problem is to minimize respect to a the function...
$\displaystyle f(a) = a - \frac{\sqrt{a^{2} - 4}}{2}\ (2)$
Kind regards
$\chi$ $\sigma$