S i m p l i f y space space colon thin space fraction numerator left parenthesis square root of 3 minus square root of 5 right parenthesis left parenthesis square root of 5 plus square root of 3 right parenthesis over denominator 7 minus 2 square root of 5 end fraction

Asked by kishor.kp14 | 20th Jun, 2019, 10:15: AM

Expert Answer:

begin mathsize 16px style fraction numerator open parentheses square root of 3 minus space square root of 5 close parentheses open parentheses square root of 5 space plus space square root of 3 close parentheses over denominator 7 space minus space 2 square root of 5 end fraction
equals space fraction numerator open parentheses square root of 3 minus space square root of 5 close parentheses open parentheses square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 5 end style begin display style space end style close parentheses over denominator open parentheses 7 space minus space 2 square root of 5 close parentheses end fraction
equals space fraction numerator begin display style open parentheses square root of 3 close parentheses squared end style begin display style space end style begin display style minus end style begin display style begin display style open parentheses square root of 5 close parentheses end style squared end style begin display style space end style over denominator open parentheses 7 space minus space 2 square root of 5 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space.... space since 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
equals space fraction numerator 3 space minus space 5 over denominator 7 space minus space 2 square root of 5 end fraction cross times fraction numerator 7 space plus space 2 square root of 5 over denominator 7 space plus space 2 square root of 5 end fraction
equals space fraction numerator negative 2 open parentheses 7 space plus space 2 square root of 5 close parentheses over denominator 49 space minus space 20 end fraction space space space.... space since 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
equals space fraction numerator negative 14 space minus space 4 square root of 5 over denominator 29 end fraction end style

Answered by Yasmeen Khan | 20th Jun, 2019, 10:42: AM