If the arithmetic mean of two numbers x and y is 11 and the geometric mean of the same two number is

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02 Feb 2022 Number System

If the arithmetic mean of two numbers x and y is 11 and the geometric mean of the same two number is 4√7. The numbers x= ? (Given, x > y)

OPtion

1) 16
2) 12
3) 14
4) 18
5) 11
6) 10
7) 8
8) 9
9) 7
10) None of these

Solution

Give, Arithmetic Mean=11, => (x+y)/2 = 11
x + y = 22 ---(1)
Geometric Mean=4√7, => √(xy) = 4√7
xy=112
Now, (x - y)² = (x + y)² - 4xy = 22² - 4*112 = 36
x - y = 6 ---(2)
Solving eqn. (1) & (2), we get x =14, y=8
So, the required number is 14.

Correct Option: 3 Best Solution (2)