Given that (p = 1 + sqrt{2}) and (q = 1 – sqrt{2}), evaluate (frac{p^{2} – q^{2}}{2pq}).
-
A.
2(2+√2) -
B.
-2(2+√2) -
C.
2√2 -
D.
-2√2
Correct Answer: Option D
Explanation
(frac{p^{2} – q^{2}}{2pq} = frac{(p + q)(p – q)}{2pq})
= (frac{(1 + sqrt{2} – (1 – sqrt{2}))(1 + sqrt{2} + 1 – sqrt{2})}{2(1 + sqrt{2})(1 – sqrt{2})})
= (frac{(2sqrt{2})(2)}{-2})
= (-2sqrt{2})