Question

determine the rational no p and q if 7+ root 5/7-root 5 - 7-root 5/7+root 5=p-7root 5q

Answer 1

Well, first you need to simplify your expression.

How ?
Simple! By rationalising.

(7+√5)/(7-√5) - (7-√5)/7+√5)

Rationalise both the terms

(7+√5)² - (7-√5)²/ 49 - 5
= 49 + 14√5 + 5 - 49 + 14√5 - 5/ 44
= 28√5/44
= 7√5/11

Now, 7√5/11 = a + (7/11) √5b

On comparison,
a = 0
b = 1

Answer 2

Answer p=0 and q=11/4