Question : If $4x=\sqrt5+2$, then the value of $(x-\frac{1}{16x})$ is:
Option 1: 1
Option 2: –1
Option 3: 4
Option 4: $2\sqrt5$
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Correct Answer: 1
Solution : Given: $4x=\sqrt5+2$ ⇒ $\frac{1}{4x}=\sqrt5-2$ (by rationalising) ⇒ $4x - \frac{1}{4x}=(\sqrt5+2)-(\sqrt5-2)$ ⇒ $4x - \frac{1}{4x}=\sqrt5+2-\sqrt5+2$ ⇒ $4x - \frac{1}{4x}=4$ Dividing both sides by 4, we get, ⇒ $\frac{4x}{4}-\frac{1}{4x×4}=\frac{4}{4}$ $\therefore x - \frac{1}{16x}=1$ Hence, the correct answer is 1.
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