Answer:
The three consecutive POSITIVE ODD integers are: 3, 5 and 7
Explanation:
If x is an integer, then there consecutive positive odd integers are:
x , x + 2, x + 4 are three consecutive integers.
Where
First integer, a = x
Second integer, b = x + 2
Third integer, c = x + 4
We are told to:
Find three consecutive POSITIVE ODD integers such that when you multiply the first and third the result is nine less than six times the second integer.
Hence, this is represented as:
a × c = 6(b) - 9
Where
a = x
b = x + 2
c = x + 4
x (x + 4 ) = 6(x + 2) - 9
x ² + 4x = 6x + 12 - 9
x² +4x - 6x - 12 + 9= 0
x² - 2x - 3 = 0
Factorising
x² +x - 3x - 3 = 0
x (x + 1) -3(x + 1) = 0
(x - 3) (x + 1) = 0
x - 3 = 0
x = 3
x + 1 = 0
x = -1
Since, x cannot be negative for this question, x = 3
First integer, a = x = 3
Solving for:
Second integer, b = x + 2
b = 3 + 2 = 5
Solving for :
Third integer, c = x + 4
c = 3 + 4 = 7
Therefore, the three consecutive POSITIVE ODD integers are: 3, 5 and 7