Value of \\sqrt{6+\sqrt{6+\\sqrt{6+........}}is

Haryana Police Constable Model Paper 2

Question : 5 of 100

Marks: +1, -0

Value of

\√{6+√{6+\√{6+........}}}

Solution:

Let

\X =\√{6+\√{6+\√{6+....}}}

\X^{2}=6+\√{6+\√{6+.......}}

\X\ ^{2}=6+ \X

\X ^{2}-\ \X -6=0

\X ^{2}-3 \X +2 \X -6=0

\X ( \X -3)+2( \X -3)=0

\X =3

\X =-2

A square root of any positive value cannot be negative.
Hence X = 3

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