Answer:
8 and 9
Step-by-step explanation:
Let the two consecutive integers be x - 1 and x
Smaller = x-1
Largere = x
If the square of the smaller integer is nineteen more than five times the larger integer, then;
(x-1)² = 19 + 5x
Expand
x²-2x+1= 19+5x
x²-2x-5x+1-19 -0
x²-7x-18 =0
Factorize
x²-9x+2x-18 =0
x(x-9)+2(x-9) = 0
(x+2) = 0 and x - 9 = 0
x = -2 and 9
SInce x cannot be negative;
x = 9
Smaller number = 9-1
Smaller number = 8
Hence the two consecutive integers are 8 and 9
