Question
Download Solution PDF\(\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+...}}}}}=?\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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।
Last updated on Mar 21, 2025
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