Question 53

If $$2x^2 - 8x - 1 = 0$$, then what is the value of $$8x^3 - \frac{1}{x^3}?$$

Solution

$$2x^2-8x-1=0$$

$$2x^2-1=8x$$

$$2x-\frac{1}{x}=8$$........(1)

Cubing on both sides,

$$8x^3-\frac{1}{x^3}-3.2x.\frac{1}{x}\left(2x-\frac{1}{x}\right)=512$$

$$8x^3-\frac{1}{x^3}-6\left(8\right)=512$$ [From (1)]

$$8x^3-\frac{1}{x^3}-48=512$$

$$8x^3-\frac{1}{x^3}=560$$

Hence, the correct answer is Option A

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