Question 67

If $$p + \left(\frac{1}{p}\right) = 2$$ find the value of $$p \times p \times p$$

Solution

Given, $$p+\left(\frac{1}{p}\right)=2$$

$$\Rightarrow$$ $$p^2+1=2p$$

$$\Rightarrow$$ $$p^2-2p+1=0$$

$$\Rightarrow$$ $$\left(p-1\right)^2=0$$

$$\Rightarrow$$ $$p-1=0$$

$$\Rightarrow$$ $$p=1$$

$$\therefore\ $$ $$p\times p\times p=1\times1\times1=1$$

Hence, the correct answer is Option C

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