5+root 11/3+2 root 11=a+(b root 11)

Asked by Aashna | 25th May, 2016, 08:24: PM

Expert Answer:

begin mathsize 16px style fraction numerator 5 plus square root of 11 over denominator 3 plus 2 square root of 11 end fraction equals a plus b square root of 11
M u l t i p l y i n g space t h e space n u m e r a t o r space a n d space d e n o m i n a t o r space b y space r a t i o n a l i s a t i o n space f a c t o r space o f space d e n o m i n a t o r comma space w e space g e t
fraction numerator 5 plus square root of 11 over denominator 3 plus 2 square root of 11 end fraction
equals fraction numerator 5 plus square root of 11 over denominator 3 plus 2 square root of 11 end fraction cross times fraction numerator 3 minus 2 square root of 11 over denominator 3 minus 2 square root of 11 end fraction
equals fraction numerator 5 cross times 3 minus 5 cross times 2 square root of 11 plus 3 cross times square root of 11 minus 2 cross times square root of 11 cross times square root of 11 over denominator open parentheses 3 close parentheses squared minus open parentheses 2 square root of 11 close parentheses squared end fraction
equals fraction numerator 15 minus 10 square root of 11 plus 3 square root of 11 minus 22 over denominator 9 minus 44 end fraction
equals fraction numerator negative 7 minus 7 square root of 11 over denominator negative 35 end fraction
equals fraction numerator negative 7 open parentheses 1 plus square root of 11 close parentheses over denominator negative 35 end fraction
equals fraction numerator 1 plus square root of 11 over denominator 5 end fraction
equals 1 fifth plus 1 fifth square root of 11
equals a plus b square root of 11
H e n c e comma space a equals 1 fifth space a n d space b equals 1 fifth end style

Answered by Rashmi Khot | 26th May, 2016, 09:23: AM

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