find the value of square root of 8 plus square root of 8 plus square root of 8... end root end root end root

Asked by apurva151 | 14th Jul, 2015, 08:09: PM

Expert Answer:

L e t space x equals square root of 8 plus square root of 8 plus square root of 8 plus... end root end root end root... left parenthesis 1 right parenthesis S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma x squared equals open parentheses square root of 8 plus square root of 8 plus square root of 8 plus... end root end root end root close parentheses squared rightwards double arrow x squared equals 8 plus square root of 8 plus square root of 8 plus... end root end root rightwards double arrow x squared equals 8 plus x rightwards double arrow x squared minus 8 minus x equals 0 rightwards double arrow x squared minus x minus 8 equals 0 S o l v i n g space b y space q u a d r a t i c space f o r m u l a comma space w e space h a v e comma x equals fraction numerator negative open parentheses negative 1 close parentheses plus-or-minus square root of open parentheses negative 1 close parentheses squared minus 4 cross times open parentheses negative 8 close parentheses cross times 1 end root over denominator 2 cross times 1 end fraction rightwards double arrow x equals fraction numerator 1 plus-or-minus square root of 33 over denominator 2 end fraction S i n c e space x space i s space t h e space s q u a r e space r o o t space o f space a space n u m b e r comma space apostrophe x apostrophe space s h o u l d space b e space p o s i t i v e. T h u s comma space x equals fraction numerator 1 plus square root of 33 over denominator 2 end fraction

Answered by Vimala Ramamurthy | 15th Jul, 2015, 10:41: AM

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