Question Number 195560 by York12 last updated on 05/Aug/23
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Commented by mr W last updated on 05/Aug/23
$${why}\:{did}\:{you}\:{delete}\:{the}\:{question}\:{sir}? \\ $$
Answered by mr W last updated on 05/Aug/23
$${no}\:{maximum}\:{exists}! \\ $$$${just}\:{consider}\:{b}={c}\rightarrow\mathrm{0}^{+} , \\ $$$${a}=\frac{\mathrm{3}−{bc}}{{b}+{c}}\rightarrow+\infty \\ $$$$\Rightarrow\left({a}+{b}+{c}\right)\rightarrow+\infty \\ $$$${that}\:{is}\:{to}\:{say}\:{that}\:{i}\:{can}\:{make}\:\left({a}+{b}+{c}\right)\: \\ $$$${reach}\:{any}\:{large}\:{value}\:{you}\:{give}. \\ $$
Commented by mr W last updated on 06/Aug/23
$${the}\:{deleted}\:{question}\:{was}: \\ $$$${for}\:{a},{b},{c}\:\geqslant\mathrm{0}\:{with}\:{ab}+{bc}+{ca}=\mathrm{3},\:{find} \\ $$$${the}\:{maximum}\:{of}\:{a}+{b}+{c}. \\ $$