Sir, how can we solve this?

Asked by agzen | 2nd Nov, 2014, 12:52: PM

Expert Answer:

L e t space x equals square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus..... end root end root end root end root end root end root end root.... left parenthesis 1 right parenthesis S q u a r i n g space o n space b o t h space t h e space s i d e s space o f space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma x squared equals square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus..... end root end root end root end root end root end root end root rightwards double arrow x squared equals 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus..... end root end root end root end root end root end root rightwards double arrow x squared minus 1 equals 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus..... end root end root end root end root end root end root rightwards double arrow fraction numerator x squared minus 1 over denominator 2 end fraction equals square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus 2 square root of 1 plus..... end root end root end root end root end root end root F r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma rightwards double arrow fraction numerator x squared minus 1 over denominator 2 end fraction equals x rightwards double arrow x squared minus 1 equals 2 x rightwards double arrow x squared minus 2 x minus 1 equals 0 S o l v i n g space t h e space a b o v e space q u a d r a t i c space e q u a t i o n space w e space h a v e comma x equals fraction numerator 2 plus-or-minus square root of 2 squared minus 4 open parentheses minus 1 close parentheses cross times 1 end root over denominator 2 cross times 1 end fraction rightwards double arrow x equals fraction numerator 2 plus-or-minus square root of 4 plus 4 end root over denominator 2 end fraction rightwards double arrow x equals fraction numerator 2 plus-or-minus square root of 8 over denominator 2 end fraction rightwards double arrow x equals fraction numerator 2 plus-or-minus 2 square root of 2 over denominator 2 end fraction rightwards double arrow x equals 1 plus-or-minus square root of 2

Answered by Vimala Ramamurthy | 3rd Nov, 2014, 09:00: AM