Question 54373
A positive number is three more than twice another number. Their product is 10 more than the square of the smaller number. Find the numbers.
ans:let the two numbers be x and y.
then according to the problem x = 2*y+3
       it is clear from the above expression that x > y  (it can be checked by putting y = 0,1,2...)
hence from the problem we can write that 
                          x*y = y^2+10 
                     (2*y+3)*y=y^2+10
                      2y^2+3y=y^2+10
                      y^2+3y-10=0
                      y^2+5y-2y-10=0
                      y(y+5)-2(y+5)=0
                      (y-2)(y+5) = 0
                       y = 2 or -5
                  and  x = 7 or -7
hence hence the two numbers are either ( 7 and 2 ) or (-5 and -7)