If a + b = 2, ab = 1 what is the value of (a, b)?

Question: If a + b = 2, ab = 1 what is the value of (a, b)?

Solution:
Given that
a + b = 2...........(1)
ab = 1..................(2)

From (1)
b = 2 - a

Putting the value in (2), we get
a(2 - a) = 1
2a - a² = 1
2a = 1 + a²
a² - 2a + 1 = 0
(a - 1)² = 0
a - 1 = 0
a = 1

a = 1 Putting the value in (2), we get
1.b = 1
b = 1

(a, b) = (1,1)