Answer:
9 and 11
OR
-9 and -11
Step-by-step explanation:
let x be the one odd integer
The pattern of numbers go: odd - even - odd - even
The next consecutive odd integer would be x + 2
"Product" means multiplying. Write "the product of two consecutive odd integers with a product of 99" as an algebraic statement:
x(x+2)=99 Distribute over brackets
x² + 2x = 99 Rearrange the equal 0
x² + 2x - 99 = 0
Remember a quadratic equation is ax² + bx + c = 0
(Equate to 0 to use quadratic formula)
State values for quadratic formula from simplified quadratic equation
a = 1; b = 2; c = -99
Use the quadratic formula.
[tex]x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]
Substitute the values of "a", "b", and "c"
[tex]x=\frac{-2±\sqrt{2^{2}-4(1)(-99)}}{2(1)}[/tex] Simplify
[tex]x=\frac{-2±\sqrt{400}}{2}[/tex] Solve the root
[tex]x=\frac{-2±20}{2}[/tex]
Split the equation at the ±
[tex]x=\frac{-2+20}{2}[/tex]
[tex]x=\frac{18}{2}[/tex]
x = 9 Possible integer solution
[tex]x=\frac{-2-20}{2}[/tex]
[tex]x=\frac{-22}{2}[/tex]
x = -11 Possible integer solution
Integers include all positive and negative whole numbers, and 0. Both positive and negative answers are possible in this problem.
Use "x+2" to get the consecutive integer from the initial possible values for "x".
If x = 9:
x+2 = x+9 = 11
9 and 11
If x = -11:
x+2 = -11+2 = -9
-9 and -11
See if your answers make sense:
9 X 11 = 99
-9 X -11 = 99
Both are possible solutions.
