Question 67

If $$p+\frac{1}{p}=112$$, find $$(p-112)^{15}+\frac{1}{p^{15}}$$

Solution

Given, $$p+\frac{1}{p}=112$$

$$\Rightarrow$$ $$p-112=-\frac{1}{p}$$

$$(p-112)^{15}+\frac{1}{p^{15}}=\left(-\frac{1}{p}\right)^{15}+\frac{1}{p^{15}}$$

$$=-\frac{1}{p^{15}}+\frac{1}{p^{15}}$$

$$=0$$

Hence, the correct answer is Option D

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