Question : If $\small c+\frac{1}{c}=3$, then the value of $\left (c-3 \right )^{7}+\frac{1}{c^{7}}$ is:
Option 1: 2
Option 2: 0
Option 3: 3
Option 4: 1
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Correct Answer: 0
Solution :
Given: $c+\frac{1}{c}=3$
$⇒ c-3 =-\frac{1}{c}$----------(1)
Now, $\left (c-3 \right )^{7}+\frac{1}{c^{7}}$
Substituting the value of equation 1, we get,
$= (-\frac{1}{c})^{7}+\frac{1}{c^{7}}$
$=-\frac{1}{c^{7}}+\frac{1}{c^{7}}$
$=0$
Hence, the correct answer is 0.
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