Find Two Consecutive Positive Integers, Sum of whose Squares is 365.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

To find: two consecutive positive integers, sum of whose squares is 365.

Let the first number be ‘a’ and the second number be ‘a+1’.

Now, according to the given statement: a²+ (a+1)² = 365

a² +( a + 1)² = 365

a² + (a² + 2a + 1) = 365 [ we know that, (a + b)² = a² + 2ab + b²]

2a² + 2a + 1 = 365

2a² + 2a + 1- 365 = 0

2a² + 2a – 364 = 0

2(a² + a – 182) = 0

a² + a – 182 = 0

a² + 14a – 13a – 182 = 0

a (a + 14) – 13 (a + 14) = 0

(a – 13) (a + 14) = 0

a – 13 = 0 and a + 14 = 0

a = 13 and a = – 14

Therefore, the two consecutive positive integers, sum of whose squares is 365 are 13 and 14.

Table of content

1. Two Consecutive Positive Integers, Sum of whose Squares is 365
2. Find Two Consecutive Positive Integers, Sum of whose Squares is 365.

Two Consecutive Positive Integers, Sum of whose Squares is 365

13 and 14 are the the two consecutive positive integers, sum of whose squares is 365. The collection of positive numbers and negative numbers are called integers. In integers, the positive numbers are known as positive integers whereas the negative numbers are called negative integers.

Example of integers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, and so on.

Key Points about Integers

On the number line, the entire positive integer range is to the right of zero, while the entire negative range is to the left.
Since all non-negative integers are whole numbers, all operations on them are carried out in the same way as they would be for whole numbers.
When combining two negative numbers, the negative sign is kept with the sum while the corresponding positive numbers are added.
Negative and positive integers can be added by subtracting the smaller of the two by their respective numerical values, then taking the sign of the larger of the two.
In order to subtract an integer from a given integer, we first multiply the inputted integer by its additive inverse.

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