Maths · Relation between A.M and G.M
Assertion are three unequal positive numbers. STATEMENT-1: The product of their
Assertion \( a, b, c \) are three unequal positive numbers. STATEMENT-1: The product of their sum and the sum of their reciprocals exceeds 9 Reason STATEMENT-2: AM of \( n \) positive numbers exceeds their HM.
- A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
- B. Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct explanation for Statement-
- C. Statement-1 is True, Statement-2 is False
- D. Statement-1 is False, Statement-2 is True
Step-by-step solution
For three unequal positive numbers a, b, c, by AM-HM inequality (AM > HM), we have (a+b+c)/3 > 3/(1/a+1/b+1/c) => (a+b+c)(1/a+1/b+1/c) > 9. Thus Statement-1 is true. Statement-2 is a general fact: AM > HM for unequal positive numbers. Since this directly implies Statement-1, it is a correct explanation.