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Statement 1 If a,b,c are three positive ...

Statement 1 If a,b,c are three positive numbers in GP, then `((a+b+c)/(3))((3abc)/(ab+bc+ca))=(abc)^((2)/(3))`.
Statement 2 `(AM)(HM)=(GM)^(2)` is true for positive numbers.

A

Statement 1 is true, Statement 2 is true, Statement 2 is a corrct explanation for Statement 1.

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

C

Statement 1 is true, Statement 2 is false.

D

Statement 1 is false, Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
C
If a,b, be two real positive and unequal numbers, then `AM=(a+b)/(2),GM=sqrt(ab)` and`HM(2ab)/(a+b)`
`:.(AM)(HM)=(GM)^(2)`
This result will be true for n numbers, if they are in GP.
Hence, Statement 1 is true, Statement 2 is false.
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