Question

Three consecutive odd integers are such that the square of the third integer is 1515 greater than greater than the sum of the squares of the first two. one solution is 33​, 55​, and 77. find three other consecutive odd integers that also satisfy the given conditions.

Answer 1

Let
x-----------> first odd integer
x+2--------> second consecutive odd integer
x+4-------> third consecutive odd integer

we know that
(x+4)²=15+x²+(x+2)²-------> x²+8x+16=15+x²+x²+4x+4
x²+8x+16=19+2x²+4x-------> x²-4x+3
x²-4x+3=0

using a graph tool----------> to calculate the quadratic equation
see the attached figure
the solution is
x=1
x=3

the answer is
the first odd integer x is 1
the  second consecutive odd integer x+2 is 3
the third consecutive odd integer x+4 is 5