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Let x be the HM and y be the GM of two positive numbers m and n . If 5 x=4 y , then which one of the following is correct?

Options

  1. A5 m=4 n
  2. B2 m=n
  3. C4 m=5 n
  4. Dm=4 n

Correct answer

D. m=4 n

Step-by-step solution

aligned & x= 2 m n m+n and y= m n & 5 x=4 y aligned A.M. of m and n= m+n 2 As 5 (2 m n) m+n =4 m n aligned & 5 m n 2 m n =m+n & 5 2 m n =(m+n) aligned 5 2 = m n + n m Let m n =K, then 5 2 =K+ 1 K 2 (K^2+1 )=5 K aligned & 2 K^2-5 K+2=0 & (K-2)(2 K-1)=0 aligned array rlrl & K & =2 or 1 2 & & m n =2 & m=4 n & or, m n = 1 2 & n=4 m array

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