Question 594589
2 positive numbers are consecutive odd integers. The square of the smaller is 10 less than 5 times the larger. Find the intergers


let x be the smaller and y , the larger. 
 x and y are consecutive odd intergers, means there is a number a ( an integer)  such that
 x= 2a +1  and y = x+2 = 2a +3
The square of the smaller is 10 less than 5 times the larger, means 
  x^2 = 5(y^2)-10  -->  (2a+1)^2 = 5(2a+3)-10
                   -->4a^2 +4a +1 = 10a +15 -10
                   -->  4a^2 +4a -10a +1 -15 +10=0
                   --> 4a^2 -6a -4=0
                   --> a^2 -(3/2)a -1 =0
                   --> (a-2)(a+1/2)=0
                   --> a = 2   ( a can not be a negative number)

so, x= 2(2)+1 = 5    and y = 2(2)+3 = 7

so, those numbers are 5 and 7