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If the ratio of A M to G M of two positive numbers a and b is 5: 3 , then a : b is equal to

Options

  1. A3: 5
  2. B2: 9
  3. C9: 1
  4. D5: 3

Correct answer

C. 9: 1

Step-by-step solution

A.M of two numbers a , b = a + b 2 G.M of two numbers a , b = ab . Given, A.M G.M = 5 3 ( a + b 2 ) ab = 5 3 a + b ab = 10 3 a ^2+ b ^2+2 ab ab = 100 9 (Squaring on both sides) 9 a^2+9 b^2+18 a b=100 a b 9 a^2-82 a b+9 b^2=0 9 a^2-81 a b-a b+9 b^2=0 9 a ( a -9 ~b )- b ( a -9 ~b )=0 (9 a - b )( a -9 ~b )=0 9 a - b =0 ; a -9 ~b =0 b =9 a ; a =9 ~b a b = 1 9 ; a b = 9 1

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