Given:
The product of two consecutive numbers is 72.
To find:
The two numbers by using the quadratic equation.
Solution:
Let the two consecutive numbers are x and (x+1).
The product of two consecutive numbers is 72.
[tex]x(x+1)=72[/tex]
[tex]x^2+x-72=0[/tex]
Splitting the middle term, we get
[tex]x^2+9x-8x-72=0[/tex]
[tex]x(x+9)-8(x+9)=0[/tex]
[tex](x+9)(x-8)=0[/tex]
Using zero product property, we get
[tex]x+9=0[/tex] and [tex]x-8=0[/tex]
[tex]x=-9[/tex] and [tex]x=8[/tex]
If [tex]x=-9[/tex], then
[tex]x+1=-9+1[/tex]
[tex]x+1=-8[/tex]
If [tex]x=8[/tex], then
[tex]x+1=8+1[/tex]
[tex]x+1=9[/tex]
Therefore, the two consecutive numbers are either 8,9 or -9,-8.
