Answer:
Let's assume that the two numbers are x and y, where x is greater than y.
From the given information, we can write two equations:
x^2 + y^2 = 85 (Equation 1)
x - y = 1 (Equation 2)
We can solve Equation 2 for x and substitute into Equation 1:
x = y + 1
(x = y + 1) into (Equation 1)
(y + 1)^2 + y^2 = 85
Simplifying this equation, we get:
2y^2 + 2y - 84 = 0
Dividing both sides by 2, we get:
y^2 + y - 42 = 0
Factoring this equation, we get:
(y + 7)(y - 6) = 0
Therefore, y = -7 or y = 6. Since x is greater than y, we can ignore the negative value.
So, y = 6 and x = y + 1 = 7.
Therefore, the two numbers are 6 and 7.