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Statement 1 a+b+c=18(a,b,cgt0), then the...

Statement 1 `a+b+c=18(a,b,cgt0)`, then the maximum value of abc is 216.
Statement 2 Maximum value occurs when `a=b=c`.

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct 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:
A
Statement 1 `a+b+c=18,a,b,cgt0`
Applying `AM ge GM` for a,b,c
`(a+b+c)/(3)ge root(3)sqrt(abc) implies root(3)sqrt(abc)le 6 implies abc le 216`
Maximum value of abc is 216 which occurs at `a=b=c`. Statement 2 is the correct explanation for Statement 1.
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