The sum of the squares of two consecutive integers is 1,201. What are the two integers ?

Question

I need the equation from the problem. The standard form , the steps of how you solved it , and the meaning of answer.

Answer 1

Let the first number be X and the 2nd number be Y

then X² + Y² = 1201 to satisfy the problem statement. Now note that Y is a consecutive number of X such that

Y = X + 1 , substitute the value of Y in the equation you get X² + ( X +1)² = 1201

Expand the equation you get X² + X² + 2 X + 1 = 1201 , then 2X ² + 2x + 1 = 1201, and

2X² + 2X -1200 = 0, Simplify , divide all terms by 2, you get X² + X - 600 = 0 solve for X

X = -1 ± √ (1)2-4(1)(-600) / 2, X = -1 ± √2401 / 2, X = -1 ± 49 /2 ,

X = (-1 + 49) /2 = 24 , and X = (-1 - 49) /2 = -50, the negative value drops out then X = 24

and Y = X +1 = 24 + 1 = 25 , note that Y is a consecutive number of X

Check X² + Y² = 1201, (24)² + ( 25)² = 576 + 625 = 1201