Answer:
3, 5, 7
Step-by-step explanation:
Let the first of the three positive consecutive odd numbers be [tex]x[/tex].
Now, the second odd number = [tex]x+2\\[/tex]
And, the third odd number = [tex]x+4[/tex]
As per question statement, the multiplication of the first and third odd number is 9 lesser than the 6 times the second integer.
Writing the equation, we get:
[tex]x(x+4) = 6(x+2)-9\\\Rightarrow x^{2} +4x=6x+12-9\\\Rightarrow x^{2} +4x-6x = 3\\\Rightarrow x^{2} -2x - 3=0\\\text{Solving the above equation by factorization method:}\\\Rightarrow x^{2} -3x +x - 3=0\\\Rightarrow x(x -3) + 1(x - 3)=0\\\Rightarrow (x -3) (x+ 1)=0\\\Rightarrow x =3, -1[/tex]
As, we got a quadratic equation, so we have two solutions here.
One is positive integer and other one is negative.
So, solution is [tex]x=3[/tex]
First number is 3.
Second number is 3 + 2 = 5
Third number is 5 + 2 = 7
