Question

The product of two consecutive positive odd numbers is 483. Find the numbers.

Answer 1

Answer:

The two consecutive positive odd numbers are 21  and 23.

Step-by-step explanation:

Let 1st number = 2x +1

      2nd number=2x+3

so: (2x +1)(2x+3) = 483

4x^2 + 6x+2x+3= 483

4x^2 + 8x+3= 483

4x^2 + 8x+3-483= 0

4x^2 + 8x-480= 0

4(x^2 + 2x-120)= 0

x^2 + 2x-120= 0 /4

x^2 + 2x-120= 0

x^2 + 12x - 10x -120= 0

x(x + 12) - 10(x +12) = 0

(  x - 10 ) ( x + 12 ) = 0

(  x - 10 ) =0    or ( x + 12 ) = 0

x =10     or   x =-12

If x=10  

2x+1= 2(10)+1

       =20+1

       =21

2x+3= 2(10)+3

       =20+3

       =23

So the two consecutive positive odd numbers are 21  and 23.