Correct option is A
Given:
Arithmetic mean = 5
Geometric mean = 3
Geometric mean = 3
Let the numbers be a and b.
Formula used:
Arithmetic mean = (a + b)/2
Geometric mean = √(ab)
Arithmetic mean = (a + b)/2
Geometric mean = √(ab)
Solution:
(a + b)/2 = 5 → a + b = 10
√(ab) = 3 → ab = 9
(a + b)/2 = 5 → a + b = 10
√(ab) = 3 → ab = 9
Now, using quadratic equation:
x² − (a + b)x + ab = 0
x² − 10x + 9 = 0
x² − (a + b)x + ab = 0
x² − 10x + 9 = 0
x = [10 ± √(100 − 36)] / 2
x = [10 ± 8] / 2
x = [10 ± 8] / 2
x = 9 or 1
Hence, the two numbers are 9 and 1.
Correct answer is (a) 9, 1
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