Question Number 149296 by mathdanisur last updated on 04/Aug/21
![if a ; b > 0 find [ (((a^2 + 4)(b^2 + 9))/(ab)) ]_(min) = ?](https://www.tinkutara.com/question/Q149296.png)
$${if}\:\:\:{a}\:;\:{b}\:>\:\mathrm{0} \\ $$$${find}\:\:\:\left[\:\frac{\left({a}^{\mathrm{2}} \:+\:\mathrm{4}\right)\left({b}^{\mathrm{2}} \:+\:\mathrm{9}\right)}{{ab}}\:\right]_{\boldsymbol{{min}}} =\:? \\ $$
Answered by dumitrel last updated on 04/Aug/21
$$\mathrm{24}\:\left({pentru}\:{a}=\mathrm{2},{b}=\mathrm{3}\right) \\ $$
Commented by mathdanisur last updated on 04/Aug/21
$${Thank}\:{You}\:{Ser} \\ $$
Answered by mnjuly1970 last updated on 04/Aug/21
$$\:\:\:\:\mathrm{E}\::=\frac{\left({a}^{\:\mathrm{2}} +\mathrm{4}\right)\left({b}^{\:\mathrm{2}} +\mathrm{9}\right)}{{ab}}\:\geqslant\frac{\mathrm{2}\left(\mathrm{2}{a}\right).\mathrm{2}\left(\mathrm{3}{b}\right)}{{ab}} \\ $$$$\:\mathrm{E}_{\:{min}} =\mathrm{24} \\ $$
Commented by mathdanisur last updated on 04/Aug/21
$${Thank}\:{You}\:{Ser} \\ $$