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ICSE Class 9 Answered

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Asked by virendraems | 18 Jun, 2019, 08:45: PM
answered-by-expert Expert Answer
begin mathsize 16px style If space fraction numerator square root of 3 space plus space 1 over denominator square root of 3 space minus space 1 end fraction space equals space straight a space plus space straight b square root of 3 space then space find space the space values space of space straight a space and space straight b.
Solution colon
straight L. straight H. straight S equals space fraction numerator square root of 3 space plus space 1 over denominator square root of 3 space minus space 1 end fraction cross times space fraction numerator square root of 3 space minus space 1 over denominator square root of 3 space minus space 1 end fraction
space space space space space space space space equals fraction numerator open parentheses square root of 3 close parentheses squared space minus space 1 squared over denominator open parentheses square root of 3 space minus space 1 close parentheses squared end fraction
space space space space space space space space equals fraction numerator 3 space minus space 1 over denominator open parentheses square root of 3 close parentheses squared space minus space 2 square root of 3 space plus space 1 end fraction space space space space space space space space space space space space space space space space space space space... space left parenthesis straight a space minus space straight b right parenthesis squared space equals space straight a squared space minus space 2 ab space plus space straight b squared space and space straight a squared space minus space straight b squared space equals space open parentheses straight a space minus space straight b close parentheses open parentheses straight a space plus space straight b close parentheses
space space space space space space space space equals fraction numerator 2 over denominator 3 space minus space 2 square root of 3 space plus space 1 end fraction
space space space space space space space space equals fraction numerator 2 over denominator 4 space minus space 2 square root of 3 space end fraction
space space space space space space space space equals fraction numerator 1 over denominator 2 space minus space square root of 3 end fraction cross times fraction numerator 2 space plus space square root of 3 over denominator 2 space plus space square root of 3 end fraction
space space space space space space space space equals fraction numerator 2 space plus space square root of 3 over denominator 4 space minus space 3 end fraction
space space space space space space space space equals space 2 space plus space square root of 3
So comma space we space get
2 space plus space square root of 3 space equals space space straight a space plus space straight b square root of 3
rightwards double arrow space straight a space equals space 2 space and space straight b space equals space 1 end style
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