1.

Find the value of \(\sqrt {7 + \sqrt {7 + \sqrt {7 +\ldots } } }\)1). 2.64572). 3.10573). 3.17894). 3.1925

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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