the difference between two numbers is 48. the difference between the arithmetic mean and geometric mean of the numbers is 18. find the numbers

• 1, 49
  
  Let the numbers be x and (x+48), then
  Arithmetic Mean = [x+(x+48)] / 2 = x+24 and
  Geometric Mean = √x(x+48) = √(48x+x²)
  Difference of arithmetic mean & geometric mean = x+24 - √(48x+x²) = 18
  => x+6 = √(48x+x²)
  => (x+6)² = 48x+x²
  => x² + 12x + 36 = 48x+x²
  => 36x = 36 or x=1
  Hence the two numbers are 1 and 1+48=49
• 5 years agoHelpfull: Yes(3) No(0)