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Asked by g_archanasharma 16th December 2018, 6:09 PM
Answered by Expert
Answer:
Arithmetic mean = begin mathsize 12px style fraction numerator p plus q over denominator 2 end fraction end style and Geometric mean = begin mathsize 12px style square root of p q end root end style
Given information : begin mathsize 12px style fraction numerator p plus q over denominator 2 end fraction end style = 2×begin mathsize 12px style square root of p q end root end style   hence (p+q)2 = 16pq
p2 -(14q)p +q2 = 0  ............(1)
 
Eqn.(1) is quadratic in p, we get the roots  p = (7 ± 4√3)q
 
let us consider p = (7+4√3)q
 
hence begin mathsize 12px style p over q space equals fraction numerator 7 plus 4 square root of 3 over denominator 1 end fraction space equals space fraction numerator begin display style open parentheses 2 plus square root of 3 close parentheses squared end style over denominator 1 end fraction space equals space fraction numerator open parentheses 2 plus square root of 3 close parentheses squared over denominator open parentheses 2 plus square root of 3 close parentheses begin display style open parentheses 2 minus square root of 3 close parentheses end style end fraction space equals space fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction end style
If we consider p = (7-4√3)q , this will not satisfy the given condition p>q.
 
Hence p : q = (2+√3) : (2-√3)
 
Answered by Expert 17th December 2018, 7:43 AM
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