Question on: JAMB Mathematics - 2001
Given that \(p = 1 + \sqrt{2}\hspace{1mm}and\hspace{1mm}q = 1 -\sqrt{2},\hspace{1mm}evaluate\hspace{1mm}\frac{(p^{2} - q^{2})}{2pq}\)
A
2(2+√2)
B
-2(2+√2)
C
2√2
D
-2√2
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Correct Option: D
HINT:
\(\frac{(p^{2} - q^{2})}{2pq}=\frac{(1+\sqrt{2})^{2}}{2((1+\sqrt{2})(1-\sqrt{2}))}\)
Use difference of two squares to expand the bracket and reduce to \(\frac{2(2\sqrt{2})}{-2} = -2\sqrt{2}\)
\(\frac{(p^{2} - q^{2})}{2pq}=\frac{(1+\sqrt{2})^{2}}{2((1+\sqrt{2})(1-\sqrt{2}))}\)
Use difference of two squares to expand the bracket and reduce to \(\frac{2(2\sqrt{2})}{-2} = -2\sqrt{2}\)
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