\(\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+...}}}}}=?\) का मान ज्ञात कीजिए।

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NPCIL Assistant Grade-1 (Advance) Official Paper-II (Held On: 08 Sept, 2018)
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Answer (Detailed Solution Below)

Option 2 : 3
Free
NPCIL Assistant Grade 1 Computer Knowledge Subject Test - 01
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20 Questions 60 Marks 15 Mins

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दिया गया है:

√(6 + √(6 + √(6 + √(6 + ...)))) = ? का मान ज्ञात कीजिए।

प्रयुक्त सूत्र:

माना, x = √(6 + √(6 + √(6 + ...)))

x2 = 6 + x

गणना:

x2 = 6 + x

⇒ x2 - x - 6 = 0

द्विघात समीकरण को हल करें:

x = [1 ± √(12 - 4×1×(-6))] / (2×1)

⇒ x = [1 ± √(1 + 24)] / 2

⇒ x = [1 ± √25] / 2

⇒ x = [1 ± 5] / 2

⇒ x = 6 / 2 या x = -4 / 2

⇒ x = 3 या x = -2

चूँकि x धनात्मक होना चाहिए, इसलिए हम x = 3 चुनते हैं।

इसलिए, दिए गए व्यंजक का मान 3 है।

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