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For alpha, beta, gamma in R, let A=[(a...

For `alpha, beta, gamma in R`, let
`A=[(alpha^(2),6,8),(3,beta^(2),9),(4,5,gamma^(2))]` and `B=[(2alpha,3,5),(2,2beta,6),(1,4,2gamma-3)]` If tr(A)=tr(B), then find the value of `(1/alpha)+(1/beta)+(1/gamma)`

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We have, tr (A)=tr (B),
`:. alpha^(2)+beta^(2)+gamma^(2)=2alpha+2beta+2 gamma-3`
`implies (alpha^(2)-2alpha+1)+(beta^(2)-2beta+1)+(gamma^(2)-2gamma+1)=0`
`implies (alpha-1)^(2)+(beta-1)^(2)+(gamma-1)^(2)=0`
`implies alpha=1, beta=1, gamma=1`
`:. (alpha^(-1)+beta^(-1)+gamma^(-1))=(1+1+1)=3`
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