z2 + 9z + 18 = z2 + 6z + 3z + 18 = z(z+6) + 3(z+6) = (z+6)*(z+3)
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a2+b2+c2=x2+y2+z2 divide each side by 2 (a2+b2+c2)/2=(x2+y2+z2)/2 a+b+c=x+y+z
There appear to be 10 terms in the determinant. A determinant can only have a perfect number of terms. So something has gone wrong with the question. 1: x2 plus 1 2: xy 3: xz 4: xy 5: y2 plus 1 6: yz 7: 1 plus x2 plus y2 plus z2 8: xz 9: yz 10: z2 plus 1
(z - 6)(z - 6)
z2 - 12 + 36 is the same as z2 + 24. That's a simplification, but not a solution. There's nothing to solve, because the question doesn't give an equation. If z2+24 were equal to something, then we'd have an equation, and we would be thrilled to solve it for the value of 'z'.