Let p = (x + y + z) and q = xyz. If |x 1 1 ; 1 y 1 ; 1 1 z| is positive, then which one of the following is correct?

Question

Let p = (x + y + z) and q = xyz. If |x  1  1 ; 1  y  1 ; 1  1  z| is positive, then which one of the following is correct?

Accepted Answer

q + 2 > p. Expanding the determinant: x(yz − 1) − 1(z − 1) + 1(1 − y) = xyz − x − z + 1 + 1 − y = xyz − (x + y + z) + 2 = q − p + 2. For this to be positive: q − p + 2 > 0, i.e., q + 2 > p.

Let p = (x + y + z) and q = xyz. If |x 1 1 ; 1 y 1 ; 1 1 z| is positive, then which one of the following is correct?

Explanation

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