I f space fraction numerator 3 plus square root of 7 over denominator 3 minus square root of 7 end fraction equals a plus b square root of 7 comma end root space space space f i n d space t h e space v a l u e space o f space space a space space a n d space b

Asked by kishor.kp14 | 20th Jun, 2019, 10:20: AM

Expert Answer:

begin mathsize 16px style straight L. straight H. straight S space equals fraction numerator begin display style 3 space space plus space square root of 7 end style over denominator begin display style 3 space space minus space square root of 7 end style end fraction
space space space space space space space space space space equals space fraction numerator 3 space space plus space square root of 7 over denominator 3 space space minus space square root of 7 end fraction cross times fraction numerator 3 space space plus space square root of 7 over denominator 3 space space plus space square root of 7 end fraction
space space space space space space space space space space equals space fraction numerator begin display style open parentheses 3 space space plus space square root of 7 close parentheses squared end style over denominator 3 squared space minus space open parentheses square root of 7 close parentheses squared end fraction space space space space space space.... space since space straight a squared space minus space straight b squared equals 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 space space equals space fraction numerator 9 space plus space 7 space plus space 6 square root of 7 space space space over denominator 9 space minus space 7 end fraction space space space space space space.... space since space open parentheses straight a space plus space straight b close parentheses squared equals straight a squared space plus space straight b squared space plus space 2 ab
space space space space space space space space space space equals fraction numerator 16 plus space 6 square root of 7 space over denominator 2 end fraction
space space space space space space space space space space equals space 8 space plus space 3 square root of 7 space
rightwards double arrow space 8 space plus space 3 square root of 7 space space equals space straight a space plus straight b square root of 7 left parenthesis straight R. straight H. straight S right parenthesis
rightwards double arrow space straight a space equals space 8 space and space straight b space equals space 3 end style

Answered by Yasmeen Khan | 20th Jun, 2019, 10:28: AM