Question 560242
Let x and y be the two positive numbers

The difference between two positive numbers is 7 
{{{x-y=7}}}
{{{x=7+y}}}.............(1)
Their product is 60
{{{xy=60}}}
Put the value of x in above equation
{{{(7+y)y=60}}}
{{{7y+y^2=60}}}
{{{7y+y^2-60=0}}}
{{{y^2+7y-60=0}}}
Now solve for y
{{{y^2+12y-5y-60=0}}}
{{{y(y+12)-5(y+12)=0}}}
{{{(y+12)(y-5)=0}}}
{{{y+12=0}}} or {{{y-5=0}}}
{{{y=-12}}} or {{{y=5}}}
so
{{{y=5}}}
Put the value of y in (1)
{{{x=7+y}}}
{{{x=7+5}}}
{{{x=12}}}
x,y= 12, 5




Check
=======
The difference between two positive numbers is 7 
12-5=7
7=7
Their product is 60
12*5=60
60=60