answer of Q2

 

Asked by Chetna.lagoon | 4th Aug, 2019, 08:06: AM

Expert Answer:

begin mathsize 16px style straight N space equals space fraction numerator square root of square root of 5 space space plus space 2 end root space space plus square root of square root of 5 space space minus space 2 end root space over denominator square root of square root of 5 plus space 1 end root end fraction minus space square root of 3 space minus space 2 square root of 2 end root space

Let space square root of square root of 5 space space plus space 2 end root space space plus square root of square root of 5 space space minus space 2 end root space equals space straight A space space and space straight B equals space space square root of 3 space minus space 2 square root of 2 end root
rightwards double arrow straight N space equals space fraction numerator straight A over denominator square root of square root of 5 plus space 1 end root end fraction space minus space straight B space space space..... space left parenthesis 1 right parenthesis
Squaring space straight A comma space we space get
straight A squared space equals space open parentheses square root of square root of 5 space space plus space 2 end root space space plus square root of square root of 5 space space minus space 2 end root close parentheses squared
space space space space space space equals 2 open parentheses square root of 5 space plus space 1 close parentheses
rightwards double arrow straight A space equals space square root of 2 open parentheses square root of square root of 5 space plus space 1 end root close parentheses space space.... space left parenthesis 2 right parenthesis
Squaring space straight B comma space we space get
straight B squared equals space space open parentheses square root of 3 space minus space 2 square root of 2 end root close parentheses squared
space space space space space equals space 3 minus space 2 square root of 2
space space space space space equals space 2 space minus space 2 square root of 2 space plus space 1
space space space space space equals open parentheses square root of 2 space minus space 1 close parentheses squared
rightwards double arrow straight B space equals space square root of 2 space minus space 1 space space space space space space.... space left parenthesis 3 right parenthesis
From space left parenthesis 1 right parenthesis comma space we space have
straight N space equals space fraction numerator straight A over denominator square root of square root of 5 plus space 1 end root end fraction space minus space straight B
space space space equals space fraction numerator square root of 2 open parentheses square root of square root of 5 space plus space 1 end root close parentheses over denominator square root of square root of 5 plus space 1 end root end fraction space minus open parentheses square root of 2 space minus space 1 space close parentheses space space.... space from space left parenthesis 2 right parenthesis space and space left parenthesis 3 right parenthesis
space space space equals square root of 2 space minus space square root of 2 space plus space 1
space space space equals space 1
rightwards double arrow straight N space equals space 1

end style

Answered by Yasmeen Khan | 4th Aug, 2019, 12:50: PM