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Prove that |{:(18,,40,,89),(40 ,,89,,198),( 89,, 198,,440):}| = 3 abc -a^(3) -b^(3)-c^(3)

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Solution :`Delta = |{:(b+C,,a-b,,a),(c+a,,b-c,,b),(a+b,,c-a,,c):}|`
`=|{:(b+c,,-b,,a),(c+a,,-c,,b),(a+b,,-a,,c):}|"""[APPLYING "C_(2) toC_(2)-C_(3)"]"`
`=|{:(c,,-b,,a),(a,,-c,,b),(b,,-a,,c):}|"""[Applying "C_(1) toC_(1)+C_(2)"]"`
`=|{:(c,,a,,b),(a,,b,,c),(b,,c,,a):}|"""[INTERCHANGING " C_(2) " and "C_(3)"]"`
`=3abc -a^(3)-b^(3)-c^(3)`


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