Answer:
9 and 10
Step-by-step explanation:
To start, let's have what we know:
a and b are two consecutive positive integers
a = first integer
b = second integer, 1 greater than variable a
b = a + 1
b^2 = 19 + 9a
To solve this, we would only have to substitute values in
b^2 = 19 + 9a
(a+1)^2 = 19 + 9a
a^2 + 2a +1 = 19 + 9a
-9a -19 -19 - 9a
a^2 -7a - 18 = 0
a^2 + 2a - 9a - 18
a(a + 2) - 9(a+2) = 0
(a - 9)(a + 2) = 0
So solving this, we would get a = 9 or a = -2. Since this is supposed to be a positive integer, a will be 9.
Solving for b,
b = a + 1
= 9 + 1
= 10
Let me know in the comments if you have any questions! If you could mark this answer as brainliest, I would very much appreciate it!
