Find a and b
7+√5/7-√5 - 7-√5/7+√5 = a+7√5b

Asked by Shawn | 26th May, 2016, 08:34: PM

Expert Answer:

begin mathsize 16px style fraction numerator 7 plus square root of 5 over denominator 7 minus square root of 5 end fraction minus fraction numerator 7 minus square root of 5 over denominator 7 plus square root of 5 end fraction equals a plus 7 square root of 5 b
L. H. S. equals fraction numerator 7 plus square root of 5 over denominator 7 minus square root of 5 end fraction minus fraction numerator 7 minus square root of 5 over denominator 7 plus square root of 5 end fraction
equals fraction numerator 7 plus square root of 5 over denominator 7 minus square root of 5 end fraction cross times fraction numerator 7 plus square root of 5 over denominator 7 plus square root of 5 end fraction minus fraction numerator 7 minus square root of 5 over denominator 7 plus square root of 5 end fraction cross times fraction numerator 7 minus square root of 5 over denominator 7 minus square root of 5 end fraction
equals fraction numerator open parentheses 7 plus square root of 5 close parentheses squared over denominator open parentheses 7 close parentheses squared minus open parentheses square root of 5 close parentheses squared end fraction minus fraction numerator open parentheses 7 minus square root of 5 close parentheses squared over denominator open parentheses 7 close parentheses squared minus open parentheses square root of 5 close parentheses squared end fraction
equals fraction numerator 49 plus 14 square root of 5 plus 5 over denominator 49 minus 5 end fraction minus fraction numerator 49 minus 14 square root of 5 plus 5 over denominator 49 minus 5 end fraction
equals fraction numerator 49 plus 14 square root of 5 plus 5 minus 49 plus 14 square root of 5 minus 5 over denominator 44 end fraction
equals fraction numerator 28 square root of 5 over denominator 44 end fraction
equals fraction numerator 7 square root of 5 over denominator 11 end fraction
equals 0 plus fraction numerator 7 square root of 5 over denominator 11 end fraction
H e n c e comma space a equals 0 space a n d space b equals 1 over 11 end style

Answered by Rashmi Khot | 27th May, 2016, 12:01: PM

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