i f space a space equals space bevelled fraction numerator 3 minus square root of 5 over denominator 3 plus square root of 5 end fraction space a n d space b space equals space bevelled fraction numerator 3 plus square root of 5 over denominator 3 minus square root of 5 end fraction comma space f i n d space a squared minus b squared

Asked by hyperzeutron1234 | 20th Apr, 2020, 10:50: PM

Expert Answer:

begin mathsize 16px style straight a space equals space fraction numerator 3 minus square root of 5 over denominator 3 plus square root of 5 end fraction space and space straight b space equals space fraction numerator 3 plus square root of 5 over denominator 3 minus space square root of 5 end fraction
straight a squared minus space straight b squared equals space open parentheses fraction numerator 3 minus square root of 5 over denominator 3 plus square root of 5 end fraction cross times fraction numerator 3 minus square root of 5 over denominator 3 minus square root of 5 end fraction close parentheses squared minus space open parentheses fraction numerator 3 plus square root of 5 over denominator 3 minus square root of 5 end fraction cross times fraction numerator 3 plus square root of 5 over denominator 3 square root of plus 5 end root end fraction close parentheses squared
space space space space space space space space space space space space space space equals space open square brackets open parentheses 3 minus square root of 5 close parentheses squared over 4 close square brackets squared minus space space open square brackets open parentheses 3 plus square root of 5 close parentheses squared over 4 close square brackets squared
space space space space space space space space space space space space space space equals space fraction numerator open parentheses 3 minus square root of 5 close parentheses to the power of 4 minus open parentheses 3 plus square root of 5 close parentheses to the power of 4 over denominator 16 end fraction end style

Answered by Yasmeen Khan | 20th Apr, 2020, 11:49: PM