Question 123

If $$2x - \frac{1}{2x} = 6$$, then the value of $$x^2 + \frac{1}{16x^2}$$

Solution

$$2x - \frac{1}{2x} = 6$$
or $$x - \frac{1}{4x} = 3$$
squaring on both sides:
$$x^2 + \frac{1}{16x^2} - \frac{1}{2}$$ = 9
or $$x^2 + \frac{1}{16x^2}$$ = 19/2


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