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
Answer by mamiya(56)   (Show Source):
You can put this solution on YOUR website! 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
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