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Statement-1: If a, b are positive real n...

Statement-1: If a, b are positive real numbers such that `a^(3)+b^(3)=16`, then `a+ble4.`
Statement-2: If a, b are positive real numbers and `ngt1`, then
`(a^(n)+b^(n))/(2)ge((a+b)/(2))^(n)`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
If `0ltnlt1,` then
`(a^(n)+b^(n))/(2)le((a+b)/(2))^(n)`
`:." "((a^(3))^(1//3)+(b^(3))^(1//3))/(2)le((a^(3)+b^(3))/(2))^(1//3)implies(a+b)/(2)le((16)/(2))^(1//3)`
`implies" "a+ble4`
Hence, statement-1 is true. Also, statement-2 is true, but it is not a correct explanation for statement-1.
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