simply question no. 6 of VSAQs of cce formative assesment of chapter no. third, pg no3.16 of RD SHARMA
 

Asked by Prachi Jha | 23rd Jun, 2014, 09:50: PM

Expert Answer:

S i m p l i f y : space square root of 3 plus 2 square root of 2 end root S o l u t i o n : C o n s i d e r space t h e space g i v e n space e x p r e s s i o n comma space square root of 3 plus 2 square root of 2 end root L e t space square root of 3 plus 2 square root of 2 end root equals a plus b square root of 2 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 3 plus 2 square root of 2 equals open parentheses a plus b square root of 2 close parentheses squared rightwards double arrow 3 plus 2 square root of 2 equals a squared plus 2 b squared plus 2 square root of 2 a b N o w space c o m p a r i n g space t h e space c o e f f i c i e n t s comma space w e space h a v e a squared plus 2 b squared equals 3 space a n d space a b equals 1 space N o w comma space a b equals 1 rightwards double arrow b equals 1 over a S u b s t i t u t i n g space t h e space v a l u e space b equals 1 over a space i n space a squared plus 2 b squared equals 3 comma space w e space h a v e a squared plus 2 open parentheses 1 over a close parentheses squared equals 3 rightwards double arrow a to the power of 4 plus 2 minus 3 a squared equals 0 rightwards double arrow a to the power of 4 minus 3 a squared plus 2 equals 0 rightwards double arrow x squared minus 3 x plus 2 equals 0 comma space w h e r e space x equals a squared rightwards double arrow open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses equals 0 rightwards double arrow x minus 1 equals 0 space o r space x minus 2 equals 0 rightwards double arrow x equals 1 space o r space x equals 2 rightwards double arrow a squared equals 1 space o r space a squared equals 2 space a n d space b squared equals 1 space o r space space b squared equals 1 half rightwards double arrow a equals plus-or-minus 1 space o r space a equals plus-or-minus square root of 2 space a n d space b equals plus-or-minus 1 space o r space b equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction N e g l e c t i n g space t h e space n e g a t i v e space v a l u e s comma space w e space h a v e a equals 1 space a n d space b equals 1 o r space a equals square root of 2 space a n d space b equals fraction numerator square root of 2 over denominator 2 end fraction rightwards double arrow square root of 3 plus 2 square root of 2 end root equals 1 plus square root of 2

Answered by Vimala Ramamurthy | 24th Jun, 2014, 10:48: AM

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