Ashifur August 8, 2023 - 08:43
Problem: If x+($\frac{1}{x}$)= 3, then the value of $x^{6}+\frac{1}{x^{6}}$=?

View all: BANGLADESH BANK | ASSISTANT DIRECTOR (AD)| WRITTEN QUESTION (MATH) SOLVE | 2015

Correct Answer: ans: 322.

Explanation:

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

Now, (x^{6}+$\frac{1}{x^{6}}$= $(x^{2})^{3}+(\frac{1}{x^{2}})^{3}$

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

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

Now, $x^{2}+\frac{1}{x^{2}} =(x+\frac{1}{x})^{2}-2x\frac{1}{x}=3^{2}-2=7$

So, putting the values,

= 7$^{3}$-3×7

=> 343-21 = 322

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