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21 votes
21 votes
The sum of the squares of two consecutive integers is 25 find the integers

User KatGaea
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1 Answer

26 votes
26 votes
Answer: 3 & 4 or -4 & -3

Step-by-step 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.
User Coocood
by
2.9k points
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