Question

The sum of two numbers is 19 and their product is 48. Find the difference between the two numbers.

Answer 1

13

3+16=19
3*16=48
16-3=13

Answer 2

`x-\ first\ number\\y-\ second\ number\\\\ \left \{ {{x+y=19} \atop {xy=48}} \right. \\\\ \left \{ {{x=19-y} \atop {xy=48}} \right. \\\\substitution\ method\\\\ (19-y)y=48\\\\ 19y-y^2-48=0\\\\ -y^2+19y-48=0\\\\Factorisation:\\ -(y^2-3y-16y+48)=0\\\\ -(y-16)(y-3)=0\\\\ y=16\ \ \ or\ \ \ y=3\\\\ x=3\ \ \ or\ \ \ x=16\\\\Numbers\ are:\ 3\ and\ 16.`