Question 72

If $$x - \frac{1}{x} = 10, then x^3 - \frac{1}{x^3}$$ is equal to:

Solution

$$x - \frac{1}{x} = 10$$

Now , we have to find,

$$x^3$$ - $$\frac{1}{x^3}$$ = (x - $$\frac{1}{x}$$)($$x^2 $$+ 1 + $$\frac{1}{x^2}$$)

Calculate,

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

=>102

Hence,

result= 10 * (102 +1) = 1030

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