If x=\sqrt{5+\sqrt{5+\sqrt{5+. . .}} then which of the following is true ?

AP ICET 2016 Paper

Question : 81 of 200

Marks: +1, -0

x=√{5+√{5+√{5+. . .}}}

then which of the following is true ?

Solution:

x=√{5+√{5+√{5+......}}}=√{5+x}

⇒x^{2}=5+x⇒x^{2}-x-5=0

⇒x={1+√{1+20}}/{2(1)}={1+√{21}}/{2}=2.8

∴{5}/{2}<2.8<3

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