SSC CGL Tier II 12 Apr 2015 Paper

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Question : 19 of 100

Marks: +1, -0

If m

=√{5+√{5+√{5+....}}}

and n

=√{5-√{5-√{5-....}}},

then among the following the relation between m and n holds is

m – n + 1 = 0
m + n – 1 = 0
m + n + 1 = 0
m – n – 1 = 0

Solution:

(4) m

=√{5+√{5+√{5+....}}}

On squaring both sides,

m^{2}=5+m ⇒ m^{2}-m=5 ....(i)

Again,
n

=√{5-√{5-√{5-....}}}

On squaring both sides,

n^{2}=5-n

⇒ n^{2}+n=5

∴m^{2}-m=n^{2}+n.........(ii)

⇒(m^{2}-n^{2}\right)=m+n

⇒(m+n)(m-n)-(m+n)=0

⇒(m+n)(m-n-1)=0

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