Question 71

If $$a + \frac{1}{a} = 2$$, what is the value of $$\left(a^4 - \frac{1}{a^4}\right)$$ ?

Solution

$$a + \frac{1}{a} = 2$$

If the sum of a number and its reciprocal = 2 then the number will be 1

So, a = 1

$$\left(a^4 - \frac{1}{a^4}\right)$$

$$\left(1^4 - \frac{1}{1^4}\right)=(1-1)=0$$

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