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)
More Arithmetic Progression Questions
15.99% of 549.99 ÷ 11.17 = ? ÷ 20.15
74.91% of 639.95 – 599.98% of 45 + 119.987 = ?
(4.88 × 5.76)2 - ?2 = 39.89 × 19.86
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exactvalue.)
(1800.23 ÷ 29.98) + (816.32 ÷ 23.9) + 1634.11 = ?
1449.98 ÷ 50.48 × 10.12 = ? × 2.16
36.05 × 5.02 + 12.052 = ? + 9.09 × 4.04Â
(31.9)3 + (34.021)² - (16.11)3 - (42.98)² = ?
