Given that \(p = 1 + \sqrt{2}\) and \(q = 1 - \sqrt{2}\), evaluate \(\frac{(p^2 - q^2)}{2pq}\).
Question 1 Report
Given that \(p = 1 + \sqrt{2}\) and \(q = 1 - \sqrt{2}\), evaluate \(\frac{(p^2 - q^2)}{2pq}\).
Answer Details
First, let's evaluate p^2 and q^2:
p^2 = (1+√2)^2 = 1 + 2√2 + 2 = 3 + 2√2
q^2 = (1-√2)^2 = 1 - 2√2 + 2 = 3 - 2√2
Next, let's substitute the values of p^2 and q^2 into the expression (p^2 - q^2)/(2pq):
(p^2 - q^2)/(2pq) = ((3 + 2√2) - (3 - 2√2))/(2(1+√2)(1-√2))
= (4√2)/(2(1-2))
= (4√2)/(-2)
= -2√2
Therefore, the answer is -2√2.
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