Question

find two consecutive positive odd numbers the sum of square is 74

Answer 1

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