Explanation

Expanding (x+z−y)(x−z+y) = x² − (z−y)² = x² − y² − z² + 2yz, and setting this proportional to yz gives x² − y² − z² = (λ−2)yz for some λ. With x + y + z = k, substitute x = k − y − z to get k² − 2k(y+z) = (λ−4)yz, i.e. k² − 2k(k−x) = (λ−4)yz. This simplifies to k(2x − k) = (λ−4)yz, and since y + z − x = k − 2x = −(2x − k), we obtain y + z − x = ((4−λ)/k)·yz. Thus y + z − x is proportional to yz, option (c).