Answer:
Step-by-step explanation:
a + b = 8......a = 8 - b
a^2 + b^2 = ab + 19
(8 - b)^2 + b^2 = b(8 - b) + 19
(8 - b)(8 - b) + b^2 = 8b - b^2 + 19
64 - 8b - 8b + b^2 + b^2 = 8b - b^2 + 19
2b^2 - 16b + 64 = 8b - b^2 + 19
2b^2 + b^2 - 16b - 8b + 64 - 19 = 0
3b^2 - 24b + 45 = 0
3(b^2 - 8b + 15) = 0
3(b - 5)(b - 3) = 0
b - 5 = 0 b - 3 = 0
b = 5 b = 3
when b = 5 when b = 3
a + b = 8 a + b = 8
a + 5 = 8 a + 3 = 8
a = 8 - 5 a = 8 - 3
a = 3 a = 5
ur integers are 5 and 3
