If $$x+\frac{1}{x}$$​ = 42, then what is the value of $$x^3+\frac{1}{x^3}$$​ ?

Correct option is C

Given:

​$$x+\frac{1}{x} = 42$$

Formula Used:

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

Solution:

​$$(x+\frac{1}{x})^3 = 42^3$$

$$x^3+3x+3\frac{1}{x}+\frac{1}{x^3}= 74088$$

Since, $$x+\frac{1}{x} = 42$$

$$x^3+\frac{1}{x^3}+3(x+\frac{1}{x}) = 74088$$

​​​$$x^3+\frac{1}{x^3}+3\times42= 74088$$

​​$$x^3+\frac{1}{x^3}+126= 74088$$

$$x^3+\frac{1}{x^3}$$ = 74088-126

​​$$x^3+\frac{1}{x^3}$$ = 73962

Thus, correct answer is (c) 73962