If $x>1$ and $x^2+\dfrac {1}{x^2}=83$, find the value of the expression$$x^3-\dfrac {1}{x^3}$$

a) $764$

b) $750$

c) $756$

d) $760$

In this question from given I tried to approximate the value of $x$ which should just above to 9 then I tried to calculate the value of cubic expression but all options are close enough to guess. Any idea to solve it?


First, notice that


Then, use the difference of two cubes formula:


We take the positive root of $81$ because $x>1$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.