Question : If $N= \frac{(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)}$, then what is the value of $(N+\frac{1}{N})$?
Option 1: 10
Option 2: 11
Option 3: 12
Option 4: 22
Correct Answer: 22
Solution :
Given: $N= \frac{(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)}$
$\frac{1}{N}= \frac{(\sqrt6+\sqrt5)}{(\sqrt6-\sqrt5)}$
To find: $(N+\frac{1}{N})$
Putting the values, we get:
= $\frac{(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)}+\frac{(\sqrt6+\sqrt5)}{(\sqrt6-\sqrt5)}$
= $\frac{(\sqrt6-\sqrt5)^2+(\sqrt6+\sqrt5)^2}{(\sqrt6+\sqrt5)(\sqrt6-\sqrt5)}$
= $\frac{6+5-2\sqrt6\sqrt5+6+5+2\sqrt6\sqrt5}{6-5}$
= 22
Hence, the correct answer is 22.
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