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

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

• let y=sqrt(6+sqrt(6+sqrt(+...)))
  y=sqrt(y+6)
  squaring both side
  y2=y+6
  y=3
• 11 years agoHelpfull: Yes(4) No(0)
• 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
  
• 11 years agoHelpfull: Yes(1) No(0)
• 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
• 11 years agoHelpfull: Yes(0) No(0)
• sqrt(6+x)=x
  x=-2,3
  hence x=3 is ans
• 11 years agoHelpfull: Yes(0) No(0)
• d=3 is solution
  
• 11 years agoHelpfull: Yes(0) No(0)