If the arithmetic mean of two numbers is 7 and the geometric mean of the same two number is 2 radic ...........

Quantitative Aptitude ( CCS) Arithmetic progression

If the arithmetic mean of two numbers is 7 and the geometric mean of the same two number is 2√10. Then find the numbers x and y respectively, such that x > y.

2,5

10,4

6,8

12,3

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Explanation:

Given, Arithmetic Mean = 7
⇒ (x + y)/2 = 7
⇒ x + y = 14 ----(1)
And, Geometric Mean = 2√10
⇒ √xy = 2√10
⇒ xy = (2√10)² = 40
Now,
⇒ (x - y)²= (x + y)² - 4xy = 142 - (4 × 40) = 196 - 160 = 36
⇒ x - y = 6 ----(2)
Now, adding equation (1) and (2) we get
⇒ 2x = 20
⇒ x = 10
Now, by equation (1)
⇒ y = 14 - x = 14 - 10 = 4