Question 5

Find the square root of$$ \frac{a^{2}}{b^{2}}$$ +$$\frac{b^{2}}{a^{2}}$$+2

Solution

$$\frac{a^2}{b^2}+\frac{b^2}{a^2}+2$$

$$=\frac{a^4+b^4+2a^2b^2}{a^2b^2}.$$

$$=\frac{\left(a^2+b^2\right)^2}{a^2b^2}.$$

So,

$$\sqrt{\frac{a^2}{b^2}+\frac{b^2}{a^2}+2}=\frac{\left(a^2+b^2\right)}{ab}=\left(\frac{a}{b}+\frac{b}{a}\right).$$

D is correct choice.

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