Question
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2.
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4.
Answer (Detailed Solution Below)
Option 4 : $14$
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Detailed Solution
सही उत्तर $14$ है।
Key Points
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prepsnap.in • Part -AQuestion:
If $x = \frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}}$, then the value of $x$ is: / यदि $x = \frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}}$ है, तो $x$ का मान है:
1.
$7$
2.
$10$
3.
$16$
4.
$14$
Correct Answer: $14$
Rationalise: $\frac{2+\sqrt{3}}{2-\sqrt{3}} = \frac{(2+\sqrt{3})^2}{4-3} = 7 + 4\sqrt{3}$ and $\frac{2-\sqrt{3}}{2+\sqrt{3}} = 7 - 4\sqrt{3}$. Adding: $(7 + 4\sqrt{3}) + (7 - 4\sqrt{3}) = 14$. / परिमेयकरण करने पर: $\frac{2+\sqrt{3}}{2-\sqrt{3}} = \frac{(2+\sqrt{3})^2}{4-3} = 7 + 4\sqrt{3}$ और $\frac{2-\sqrt{3}}{2+\sqrt{3}} = 7 - 4\sqrt{3}$। जोड़ने पर: $(7 + 4\sqrt{3}) + (7 - 4\sqrt{3}) = 14$।
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