For distinct even integers x , y , z , let N be the minimum determinant: det 1 + x 2 + x 4 1 + x y + x 2 y 2 1 + x z + x 2 z 2 1 + x y + x 2 y 2 1 + y 2 + y 4 1 + yz + y 2 z 2 1 + x z + x 2 z 2

Question

For distinct even integers x , y , z , let N be the minimum determinant: det ​ 1 + x 2 + x 4 1 + x y + x 2 y 2 1 + x z + x 2 z 2 ​ 1 + x y + x 2 y 2 1 + y 2 + y 4 1 + yz + y 2 z 2 ​ 1 + x z + x 2 z 2 1 + yz + y 2 z 2 1 + z 2 + z 4 ​ ​ Find N /1024 .

TestHub · Accepted Answer

The determinant is ( x − y ) 2 ( y − z ) 2 ( z − x ) 2 . Its minimum for distinct even integers is 256 at ( − 2 , 0 , 2 ), so N /1024 = 1/4 .

Mathematics - Determinant Question with Solution | TestHub

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