What are the two consecutive positive integers, the sum of whose squares is 313?

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12 and 13

13 and 12

11 and 12

None of these

answer is A.

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Detailed Solution

Concept: The second number will be

if a is the smaller number. These are squared, added, and equalised to yield 313. After that, find a.
Let a be the lesser number. The second number will be a+1 because the numbers are now consecutive.
We are informed that 313 is equal to the sum of their squares.

We know,

.
We will utilize this to simplify

Putting this in equation

Dividing this by 2, we get

This equation is quadratic.
We know,

is a quadratic equation in

.
Using this, we get,

We will choose

because the question requires a positive number.
So,

Therefore, 12 and 13 are the two consecutive positive integers needed.
Hence, option 1 is correct.

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