# in the de numeris datis of jordanus nemorarius we have the following problem: the sum of two arbitrary numbers is 10. if the sum o

in the de numeris datis of jordanus nemorarius we have the following problem: the sum of two arbitrary numbers is 10. if the sum of the squares of the two numbers added to their difference is 62, what are the numbers?

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1. The two arbitrary numbers are -14 and 24
Arbitrary numbers:
Basically, the arbitrary numbers refers the numbers that have no special property, other than being large-valued.
Given,
The sum of two arbitrary numbers is 10.
And we need to find if the sum of the squares of the two numbers added to their difference is 62, what are the numbers.
Let us consider x and y be the two arbitrary numbers.
Then according to the given question,
The sum of two arbitrary numbers is 10.
And it ca be written as,
=> x +  y = 10 ————————(1)
And then we know that the sum of the squares of the two numbers added to their difference is 62,
Then
=> (x + y)² + (x – y) = 62
Here we have to apply the value of x + y on the equation then we get,
=> 10² + x – y = 62
=> 100 +(x – y) = 62
=> x – y = -38 ——————(2)
Now, we have to solve the equation (1) and (2), then we get,
The value of x as,
=> 2x = -28
=> x = -14
So, the value of y is calculated as,
=> -y = -38 + 14
=> -y = -24
=> y = 24
Therefore, the value of x is -14 and the value of y is 24.
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