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  4. If x+(1/x)=7, then x3-(1/x3) is

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Q. If $x+\frac{1}{x}=7$, then $x^3-\frac{1}{x^3}$ is

Polynomials, LCM and HCF of Polynomials

Solution:

(i) Use the formulae $(a+b)^2$ and $(a-b)^3$.
(ii) Find $x-\frac{1}{x}$ by using $(x-\frac{1}{x})^2-4=(x-\frac{1}{x})^2$.
(iii) Find $x^3-\frac{1}{2 x^3}$ by using $(x-\frac{1}{x})^3$
$+3 x \cdot(\frac{1}{x})(x-\frac{1}{x})$