Question

The sum of cubes of two consecutive positive odd integers is 468. find the integers.

Answer 1

Find two consecutive positive odd numbers such that sum of their squares is 74? 
Answer by geetha_rama(94)   (Show Source): You can put this solution on YOUR website!
Let X be a positive odd number.
Hence the next positive odd number = X+2 
X^2 + (X+2)^2 = 74 
X^2 + X^2 + 4X + 4 = 74 
2*X^2 + 4*X - 70 = 0 
X^2 + 2*X - 35 = 0 
X^2 + 7*X - 5*X - 35 = 0
X*(X+7) -5*(X+7)=0
(X+7)*(X-5)=0 
Hence X= 5, -7
Since the number is a positive odd number ,
X = 5 and the next consecutive odd number is 7
Cross Check: 5^2 + 7^2 = 25 + 49 = 74