Question

Determine rational numbers p and q if 7+ root 5 divided by 7 - root 5 = p+q root 5

Answer 1

The answer is p = 27/22 and q = 7/22.

Step-by-step explanation:

7+√5/7–√5 = p+q√5

(7+√5)(7+√5)/(7–√5)(7+√5) = p+q√5

(7+√5)²/(7)² – (√5)² = p+q√5

(7)²+2•7•√5 +(√5)² / 49–5 = p+q√5

49 + 14√5 + 5 / 44 = p+q√5

54 +14√5 /44 = p+q√5

p = 54/44 and q = 14/44

p = 27/22 and q = 7/22