Question Number 198786 by sonukgindia last updated on 24/Oct/23
Commented by Frix last updated on 24/Oct/23
$$\mathrm{If}\:{a},\:{b},\:{c},\:{d},\:{e}\:\in\mathbb{N}: \\ $$$$\mathrm{1}.\:{abc}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3} \\ $$$$\mathrm{2}.\:{bcd}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{5} \\ $$$$\mathrm{3}.\:{cde}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}×\mathrm{5} \\ $$$$\mathrm{4}.\:{dea}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{5} \\ $$$$\Rightarrow\:{d}=\mathrm{5} \\ $$$$ \\ $$$$\mathrm{1}.\:{abc}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3} \\ $$$$\mathrm{2}.\:{bc}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3} \\ $$$$\Rightarrow\:{a}=\mathrm{2} \\ $$$$ \\ $$$$\mathrm{4}.\:\Rightarrow\:{e}=\mathrm{6} \\ $$$$ \\ $$$$\mathrm{3}.\:\Rightarrow\:{c}=\mathrm{4} \\ $$$$ \\ $$$$\mathrm{1}.\:\Rightarrow\:{b}=\mathrm{3} \\ $$
Commented by mr W last updated on 24/Oct/23
$${sonukgindia}\:{sir}: \\ $$$${why}\:{don}'{t}\:{you}\:{give}\:{any}\:{feedback}\:{and} \\ $$$${never}\:{reply}\:{what}\:{other}\:{people}\:{ask} \\ $$$${you}? \\ $$
Commented by sonukgindia last updated on 24/Oct/23
$${sorry}\:{i}\:{will}\:{give} \\ $$
Commented by mr W last updated on 24/Oct/23
$${thanks}\:{for}\:{this}\:{reply}! \\ $$
Answered by Frix last updated on 24/Oct/23
$$\mathrm{One}\:\mathrm{of}\:\infty\:\mathrm{solutions}: \\ $$$${a}=\mathrm{2}\:\:{b}=\mathrm{3}\:\:{c}=\mathrm{4}\:\:{d}=\mathrm{5}\:\:{e}=\mathrm{6} \\ $$
Answered by mr W last updated on 24/Oct/23
$$\mathrm{5}\:{unknowns}:\:{A},{B},{C},{D},{E} \\ $$$${but}\:{only}\:\mathrm{4}\:{equations} \\ $$$$\Rightarrow{infinitely}\:{many}\:{solutions}! \\ $$