Question Number 214638 by mr W last updated on 14/Dec/24
$${if}\:{the}\:{sum}\:{of}\:{three}\:{prime}\:{numbers} \\ $$$${is}\:\mathrm{130},\:{what}\:{is}\:{the}\:{possible}\: \\ $$$${maximum}\:{of}\:{their}\:{product}? \\ $$
Answered by BaliramKumar last updated on 14/Dec/24
$$\mathrm{2}\:+\:{x}\:+\:{y}\:=\:\mathrm{130} \\ $$$${x}\:+\:{y}\:=\:\mathrm{128} \\ $$$${for}\:{xy}_{{max}} \:\:\:\:\Rightarrow\:\:\:\:\:\:\:{x}\:=\:{y}\:=\:\frac{\mathrm{128}}{\mathrm{2}}\:=\:\mathrm{64} \\ $$$${but}\:\mathrm{64}\:{is}\:{not}\:{prime}\:{so}\:{x}\:{and}\:{y}\:{nearest}\:{to}\:\mathrm{64} \\ $$$${x}\:=\:\mathrm{64}−\mathrm{3}\:=\:\mathrm{61} \\ $$$${y}\:=\:\mathrm{64}\:+\:\mathrm{3}\:=\:\mathrm{67} \\ $$$$\left(\mathrm{2},\:\mathrm{61},\mathrm{67}\right){Answer} \\ $$$$ \\ $$$${other}\:{pair}\:\left(\mathrm{2},\:\mathrm{19},\:\mathrm{109}\right);\:\left(\mathrm{2},\:\mathrm{31},\:\mathrm{97}\right) \\ $$
Commented by mr W last updated on 14/Dec/24
��