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Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] wh...

Let `A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)]` where `b gt 0`. Then the minimum value of `("det.(A)")/(b)` is

Text Solution

Verified by Experts

The correct Answer is:
2
`|A|=|(2,b,1),(b,b^(2)+1,b),(1,b,2)|`
`R_(1) to R_(1)-R_(3)`
`|A|=|(1,0,-1),(b,b^(2)+1,b),(1,b,2)|=1(2b^(2)+2-b^(2))-1(b^(2)-b^(2)-1)=b^(2)+3`
`(|A|)/(b)=b+(3)/(b) `
`A.M. ge G.M. `
`(b+(3)/(b))/(2) ge sqrt(3)`
`(b+(3)/(b))_("min")=2sqrt(3)`
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Knowledge Check

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