यदि X = $$\sqrt{2}+\sqrt{3}$$ एवं Y = $$\sqrt{2}−\sqrt{3}$$ है, तो $$\rm\frac{X^2+ Y^2}{XY}$$ = _________

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1. −10
2. −20
3. 10
4. 20

Answer (Detailed Solution Below)

Option 1 : −10
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Detailed Solution

दिया गया है:

X = $$\sqrt{2}+\sqrt{3}$$ और Y = $$\sqrt{2}−\sqrt{3}$$

गणना:

XY = $$(\sqrt{2}+\sqrt{3})\times (\sqrt{2}-\sqrt{3})$$ = 1

X2+Y2 = $$(\sqrt{2}+\sqrt{3})^2+(\sqrt{2}-\sqrt{3})^2$$ = 2 x (2 + 3) = 10

$$\rm\dfrac{X^2+ Y^2}{XY}$$ = $$\dfrac{10}{1} = 10$$

∴ उत्तर 10 है।

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