Answer and Explanation:
We can simplify the expression 7+√5 - 7-√5 as follows:
7+√5 - 7-√5 = (7 - 7) + (√5 - (-√5)) = 2√5
Therefore, we have:
7+√5 - 7-√5 = 2√5
To express this as a fraction in the form of p - q√5, we can multiply both the numerator and denominator by the conjugate of the denominator:
(2√5)(7+√5) / (7+√5)(7-√5)
Simplifying this expression gives us:
(14 + 2√5) / (49 - 5) = (14 + 2√5) / 44
Therefore, p = 14 and q = 44.
Hence,
7+ √5 - 7-√5 = p-7√5 q = (14 + 2√5) / 44.