Option A:
Since 7 and 11 are both rational, the sum and difference are rational.
Solution:
Given equation:
[tex]p^{2}-14 p-72=0[/tex]
[tex]p^{2}-14 p=72[/tex]
Add 49 on both sides of the equation.
[tex]p^{2}-14 p+49=72+49[/tex]
[tex]p^{2}-7p -7 p+49=121[/tex]
[tex]p(p-7) -7( p-7)=121[/tex]
Take common factor (p - 7) outside.
[tex](p-7)( p-7)=11^2[/tex]
[tex](p-7)^2=11^2[/tex]
Taking square root on both sides.
p - 7 = ±11
p = ±11 + 7
i.e., p = 11 + 7, p = -11 + 7
11 and 7 are rational numbers.
So the sum and and difference is also rational.
Option A is the correct answer.
Since 7 and 11 are both rational, the sum and difference are rational.
