Question Number 180889 by mr W last updated on 18/Nov/22
$${the}\:{average}\:{of}\:\mathrm{10}\:{numbers}\:{is}\:\mathrm{5}.\:{the} \\ $$$${sum}\:{of}\:{their}\:{squares}\:{is}\:\mathrm{5000}.\:{how}\: \\ $$$${large}\:{can}\:{the}\:{largest}\:{number}\:{among} \\ $$$${them}\:{at}\:{most}\:{be}\:{and}\:{how}\:{small}\:{can}\: \\ $$$${the}\:{smallest}\:{number}\:{among}\:{them} \\ $$$${at}\:{most}\:{be}? \\ $$
Commented by mr W last updated on 20/Nov/22
$${the}\:{largest}\:{number}\:{can}\:{at}\:{most}\:{be} \\ $$$$\mathrm{5}+\mathrm{5}\sqrt{\mathrm{11}} \\ $$$${the}\:{smallest}\:{number}\:{can}\:{at}\:{most}\:{be} \\ $$$$\mathrm{5}−\mathrm{5}\sqrt{\mathrm{11}} \\ $$