the value of ?6+?6+?6+....

Asked by sowmya subathra | 5th Apr, 2013, 08:18: AM

Expert Answer:

Please note that the correct question would be sqrt{6 + [sqrt6+.(sqrt6+..)]}
 
To solve this, let a = sqrt{6 + [sqrt6+.(sqrt6+..)]}
then, a^2 = 6 + [sqrt6+.(sqrt6+..)]
a^2 = 6 + a  (Since, sqrt{6 + [sqrt6+.(sqrt6+..)]} an infinite series)
a^2 -a-6 = 0
(a-3) (a+2) = 0
So, a = 3 or a = -2. 

Answered by  | 7th Apr, 2013, 07:49: AM

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