Given:
p and q are the two distinct solutions to the equation
[tex](x-3)(x+3)=21x-63[/tex]
To find:
The value of p-q if p>q.
Solution:
We have,
[tex](x-3)(x+3)=21x-63[/tex]
[tex](x-3)(x+3)=21(x-3)[/tex]
[tex](x-3)(x+3)-21(x-3)=0[/tex]
[tex](x-3)(x+3-21)=0[/tex]
[tex](x-3)(x-18)=0[/tex]
Using zero product property, we get
[tex]x-3=0\text{ and }x-18=0[/tex]
[tex]x=3\text{ and }x=18[/tex]
Here, 18>3, so p=18 and q=3.
Now,
[tex]p-q=18-3[/tex]
[tex]p-q=12[/tex]
Therefore, the value of p-q is 12.
