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Let [x]= the greatest integer less than or equal to "x" .If all the values of "x" such that the product `[x-(1)/(2)][x+(1)/(2)]` is prime,belongs to the set `[x_(1),x_(2))uu[x_(3),x_(4))` ,find the value of `x_(1)^(2)+x_(2)^(2)+x_(3)^(2)+x_(4)^(2)`

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