Question 81
If $$\left(x^2 + \frac{1}{x^2}\right) = 8.25$$, what is the value of $$\left(x^3 - \frac{1}{x^3}\right)?$$
Solution
Since $$\left(x^2 + \frac{1}{x^2}\right) = 8.25$$, we can rewrite the same as $$\left(x-\ \frac{\ 1}{x}\right)^2\ +\ 2x\times\ \ \frac{\ 1}{x}$$ = 8.25
This gives us $$\left(x-\ \frac{\ 1}{x}\right)^2$$ = 6.25
Or, $$\left(x-\ \frac{\ 1}{x}\right)$$ = 2.5
Now, $$\left(x\right)^3-\ \left(\frac{\ 1}{x}\right)^3$$ =
On substituting the values, we get the answer as 30.625
