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Let a,bgt0 and alpha=(hati)/(a)+(4hatj)/...

Let a,bgt0 and `alpha=(hati)/(a)+(4hatj)/(b)+bhatk` and `beta=bhati+ahattj+(1)/(b)hatk`, then the maximum value of `(10)/(5+alpha*beta)` is

A

1

B

2

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
`vecalpha.vecbeta = b/a+(4a)/(b)+1ge5`
So, `(10/(5 + vecalpha.vecbeta))_("max")=1`.
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Knowledge Check

  • If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

    A
    `-(3)/(5)`
    B
    `(3)/(5)`
    C
    `(5)/(3)`
    D
    `-(5)/(3)`

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