Latest SSC Aptitude Question SOLUTION: sqrt (6+ sqrt(6+ sqrt (6+...))) is equal to a) 2 b) 5 c) 4 d) 3

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(#M40010958) SSC Numerical Ability question Keep an EYE

sqrt (6+ sqrt(6+ sqrt (6+...))) is equal to

a) 2 b) 5 c) 4 d) 3

Asked In SSC muthu (11 years ago)

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Read Solution (5) :

Vivek Tiwari  (11 years ago)

let y=sqrt(6+sqrt(6+sqrt(+...)))
y=sqrt(y+6)
squaring both side
y2=y+6
y=3

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Prashant  (11 years ago)

let, y=√(6+√(6+√(6+...))) ---- (i)
now,
as there are lots of(infinite times) √6 is added, so if we leave 1 of √6 (let from rightmost side), there wouldn't be any loss in sum. and,

now, the above expression become (same as above):
y= √(6+√(6+√(6+...))) ---- (ii)
now,
put the value of eqn(ii) in eqn(i)(leaving 1st √6 at its place), we get,

y= √(6+y)
squaring both side, y^2= 6+y or, y^2 -y -6=0.

On solving , we get y=-2,3 => y = +3 (as √ can't be negative) --- Ans

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akanksha upadhyay  (11 years ago)

sqrt (6+ sqrt(6+ sqrt (6+...)))=x
=> x=sqrt(6+x)
=> x^2=6+x
=>x^2-x-6=0
=>x^2-3x+2x-6=0
=>(x-3)(x+2)=0
=>x=-2,3
neglect -2
Ans=3

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RITESH SRIVASTAV  (11 years ago)

sqrt(6+x)=x
x=-2,3
hence x=3 is ans

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sc mandota  (11 years ago)

d=3 is solution

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