One positive integer is 2 less than twice another the sum of their squares is 337 find the integers
Let's call the two integers x and y.
We know that one positive integer is 2 less than twice another, so we can write one equation:
x = 2y - 2
We also know that the sum of their squares is 337, so we can write another equation:
x^2 + y^2 = 337
To solve these equations, we can substitute the value of x from the first equation into the second equation:
(2y - 2)^2 + y^2 = 337
Expanding and simplifying this equation gives:
4y^2 - 8y + 4 + y^2 = 337
Combining like terms gives:
5y^2 - 8y - 333 = 0
We can factor this quadratic equation as:
(5y + 19)(y - 7) = 0
So, either 5y + 19 = 0 or y - 7 = 0
If 5y + 19 = 0, then y = -19/5, which is not a positive integer. So we can discard this solution.
If y - 7 = 0, then y = 7. Substituting this value into the first equation gives:
x = 2(7) - 2
x = 14 - 2
x = 12
Therefore, the two integers are 12 and 7.