The arithmetic mean and geometric mean of of two numbers are 7 and 2√10 respectively, then find the numbers ..
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A.
2,20
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B.
5,4
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C.
4,10
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D.
8,5
Correct Answer:
C. 4,10
Explanation:
To find the numbers when the arithmetic mean (AM) is 7 and the geometric mean (GM) is 2√10, let the two numbers be x and y.1. Based on the definition of the arithmetic mean: (x + y) / 2 = 7 x + y = 14 2. Based on the definition of the geometric mean: √(xy) = 2√10 Squaring both sides gives: xy = (2√10)² = 4 \* 10 = 40 3. We need two numbers that add up to 14 and multiply to 40. By testing the factors of 40: 4 + 10 = 14 4 \* 10 = 40The two numbers are 4 and 10. Therefore, the correct option is C.
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