Question

Dec 23, 8:45:08 PM

Answer 1

Answer:

3, 5, 7

Step-by-step explanation:

Let the first of the three positive consecutive odd numbers be $x$.

Now, the second odd number = $x+2$

And, the third odd number = $x+4$

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:

$x(x+4) = 6(x+2)-9\\\Rightarrow x^{2} +4x=6x+12-9\\\Rightarrow x^{2} +4x-6x = 3\\\Rightarrow x^{2} -2x - 3=0\\\text{Solving the above equation by factorization method:}\\\Rightarrow x^{2} -3x +x - 3=0\\\Rightarrow x(x -3) + 1(x - 3)=0\\\Rightarrow (x -3) (x+ 1)=0\\\Rightarrow x =3, -1$

As, we got a quadratic equation, so we have two solutions here.

One is positive integer and other one is negative.

So, solution is $x=3$

First number is 3.

Second number is 3 + 2 = 5

Third number is 5 + 2 = 7