Answer:
the two integers are 11 and -8
Explanation:
Let's call the two integers we're trying to find "x" and "y".
From the problem statement, we know two things:
x + y = 3 (the sum of the two integers is three)
x^2 + y^2 = 185 (the sum of the squares is 185)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:
y = 3 - x
Now we can substitute this expression for "y" into the second equation:
x^2 + (3 - x)^2 = 185
Expanding the square on the left-hand side, we get:
x^2 + 9 - 6x + x^2 = 185
Combining like terms, we get:
2x^2 - 6x - 176 = 0
We can simplify this equation by dividing both sides by 2:
x^2 - 3x - 88 = 0
Now we can solve for "x" using the quadratic formula:
x = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)
Simplifying, we get:
x = (3 ± sqrt(361)) / 2
We can ignore the negative root, since it would give us a negative value for "y". So, taking the positive root, we get:
x = (3 + 19) / 2 = 11
Now we can use the first equation to solve for "y":
y = 3 - x = 3 - 11 = -8