Answer for this question is? 

Asked by dineshchem108 | 11th Dec, 2018, 10:21: PM

Expert Answer:

begin mathsize 16px style open parentheses 5 plus square root of 2 close parentheses straight x squared minus open parentheses 4 plus square root of 5 close parentheses straight x plus 8 plus 2 square root of 5 equals 0
Comparing space with space ax squared plus bx plus straight c equals 0
straight a equals 5 plus square root of 2 comma space straight b equals negative open parentheses 4 plus square root of 5 close parentheses comma space straight c equals 8 plus 2 square root of 5
Let space straight alpha space and space straight beta space are space the space roots space of space the space equation.
straight alpha space plus straight beta equals fraction numerator 4 plus square root of 5 over denominator 5 plus square root of 2 end fraction space and space αβ equals fraction numerator 8 plus 2 square root of 5 over denominator 5 plus square root of 2 end fraction
Harmonic space mean space equals fraction numerator 2 over denominator begin display style 1 over straight alpha end style plus begin display style 1 over straight beta end style end fraction equals fraction numerator 2 αβ over denominator straight alpha space plus straight beta end fraction
Harmonic space mean space equals fraction numerator 2 cross times fraction numerator 8 plus 2 square root of 5 over denominator 5 plus square root of 2 end fraction over denominator fraction numerator 4 plus square root of 5 over denominator 5 plus square root of 2 end fraction end fraction equals fraction numerator 2 cross times 2 open parentheses 4 plus square root of 5 close parentheses over denominator 4 plus square root of 5 end fraction equals 4 end style

Answered by Sneha shidid | 12th Dec, 2018, 09:20: AM

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