Question
1.
2.
3.
4.
Answer (Detailed Solution Below)
Option 3 : $3$ / $3$
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Detailed Solution
सही उत्तर $3$ / $3$ है।
Key Points
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prepsnap.in • Part -AQuestion:
If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \cdots}}}$ (infinite nested radicals), find the value of $x$. / यदि $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \cdots}}}$ (अनंत नेस्टेड करणी) है, तो $x$ का मान ज्ञात कीजिए।
1.
$\sqrt{6}$ / $\sqrt{6}$
2.
$2$ / $2$
3.
$3$ / $3$
4.
$6$ / $6$
Correct Answer: $3$ / $3$
Squaring gives $x^2 = 6 + x$, i.e. $x^2 - x - 6 = 0$, so $(x - 3)(x + 2) = 0$. Since $x > 0$, $x = 3$. / वर्ग करने पर $x^2 = 6 + x$, अर्थात् $x^2 - x - 6 = 0$, अतः $(x - 3)(x + 2) = 0$। चूँकि $x > 0$, इसलिए $x = 3$।
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