Question 14

What is the simplified value of $$\frac{\sqrt{5}+\sqrt{4}}{\sqrt{5}-\sqrt{4}}+\frac{\sqrt{5}-\sqrt{4}}{\sqrt{5}+\sqrt{4}}$$ ?

Solution

Expression : $$\frac{\sqrt{5}+\sqrt{4}}{\sqrt{5}-\sqrt{4}}+\frac{\sqrt{5}-\sqrt{4}}{\sqrt{5}+\sqrt{4}}$$

= $$\frac{(\sqrt5+\sqrt4)^2+(\sqrt5-\sqrt4)^2}{(\sqrt5-\sqrt4)(\sqrt5+\sqrt4)}$$

= $$\frac{(5+4+2\sqrt{20})+(5+4-2\sqrt{20})}{5-4}$$

= $$\frac{(9+9)}{1}=18$$

=> Ans - (C)

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