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if-a-b-gt-0-find-a-2-4-b-2-9-ab-min-




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

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