Question
The arithmetic mean and geometric mean of two numbers
are 7 and 2√10 respectively, then find the numbers.Solution
Arithmetic Mean = 7 (x + y)/2 = 7 x + y = 14 ----(1) Geometric Mean = 2√10 √ xy = 2√ 10 Now, xy = (2√ 10)2 = 40 ------(2) (x - y) ² = (x + y) ² - 4xy (x - y) ² = 142 - (4 x 40) (x - y) ² = 196 - 160 = 36 x - y = 6 ----(3) Now, adding equation (1) and (3) we get 2x = 20 x = 10 and y =4. (10,4)
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