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Consider the quantities such that x(1),x...

Consider the quantities such that `x_(1),x_(2),….x_(10),-1 lex_(1),x_(2)….,x_(10)le 1` and `x_(1)^(3)+x_(2)^(3)+…+x_(10)^(3)=0`, then the maximum value of `x_(1)+x_(2)+….+x_(10)` is

A

A) `10//3`

B

B) 10

C

C) `5//3`

D

D) 5

Text Solution

Verified by Experts

The correct Answer is:
A
Let `x_(i)=sin theta_(i)[i=1,2,…..,10]`
Given `sum_(i=1)^(10)(sin theta_(i))^(3)=0`
`rArr 4sum_(k=1)^(10)(sin theta_(1))^(3)=0`
`rArr 3sum_(i=1)^(10)sin theta_(1)-sum_(i=1)^(10)sin 3theta_(i)=0` (as `sin theta = 0`, then `sin 3 theta=0`)
`rArr sum_(i=1)^(10)sin theta_(i)=(1)/(3)sum_(i=1)^(10)sin 3theta_(i)le(10)/(3)`
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