Answer: 3 & 4 or -4 & -3
Explanation:
For this problem, we know that we need two consecutive integers and the sum of the squares is equivalent to 25.
So what is the square root of 25?
5
So with this, we know that our two numbers need to be less than 5, but greater than -5.
Consider the following squares:
(1)^2 = 1
(2)^2 = 4
(3)^2 = 9
(4)^2 = 16
Which of the following sums to 25?
9 + 16 = 25
So one pair of numbers is 3 and 4.
Consider that we have the set of integers. Well, the square values of the negative integers are as follows:
(-1)^2 = 1
(-2)^2 = 4
(-3)^2 = 9
(-4)^2 = 16
Notice, the sum of the squares of the consecutive integers -4 and -3 also equals 25.
Hence another pair is -4 and -3.
So there are two pairs that satisfy the stated query.
3 and 4
-4 and -3
Cheers.
