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Find the value of \(\sqrt {7 + \sqrt {7 + \sqrt {7 +\ldots } } }\)1). 2.64572). 3.10573). 3.17894). 3.1925 |
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Answer» Let x = $(\sqrt {7 + \sqrt {7 + \sqrt {7 +\ldots } } })$ ⇒ $({\RM{x}} = \sqrt {7 + {\rm{x}}})$ ⇒ x2 = 7 + x ⇒ x2 – x – 7 = 0 Hence we get, $({\rm{x}} = \frac{{1 \PM \sqrt {1 + 28} }}{2} = \frac{{1 \pm 5.385}}{2} = 3.1925,{\rm{\;}} - 2.1925)$ Since, the GIVEN term is positive, ∴ the correct answer is 3.1925. |
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