Question 62

The value of the expression $$\frac{1}{4} \left\{\left(a + \frac{1}{a}\right)^2 - \left(a - \frac{1}{a}\right)^2\right\}$$ is:

Solution

$$\frac{1}{4} \left\{\left(a + \frac{1}{a}\right)^2 - \left(a - \frac{1}{a}\right)^2\right\}$$

$$\frac{1}{4}\left\{a^2+\frac{1}{a^2}+2-\left(a^2+\frac{1}{a^2}-2\right)\right\}$$

$$\frac{1}{4}\left\{a^2+\frac{1}{a^2}+2-a^2-\frac{1}{a^2}+2\right\}$$

$$\frac{1}{4}\times4=1$$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: