For any two positive numbers, we have
a) AM>_GM
b) AM›_ GM
c) AM=3/4 GM
d) none
Answers
Answer:
a) is right answer of this question
Given : two positive numbers
To Find : Correct option
a) AM ≥ GM
b) AM ≤ GM
c) AM =3/4 GM
d) none
Solution:
Two positive number a , b
AM = (a + b)/2
GM= √ab
as we know that
(a - b)² ≥ 0
=> a² + b² - 2ab ≥ 0
=> Adding 4ab both sides
=> a² + b² + 2ab ≥ 4ab
=> (a + b)² ≥ 4ab
Taking square root both sides
=> a + b ≥ 2√ab
=> (a + b)/2 ≥ √ab
=> AM ≥ GM
option a) is correct
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