Question

Verify:a³+b³+c³-3 abc= ½(a+b+c)[(a-b)²+(b-c)²+(c-a)²]​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

LHS= RHS

Step-by-step explanation:

RHS

a/2+b/2+c/2[a²+b²-2ab+b²+c²-2bc+c²+a²-2ca]

=> a³/2+ab²/2-2a²b/2+ab²/2+ac²/2-2abc/2+ac²/2+ a³/2-2ca²/2+a²b/2+b³/2-2ab²/2+b³/2+bc²/2 - 2b²c/2+ bc²/2+a²b/2-2abc/2+ca²/2+b²c/2-2abc/2+b²c/2+c³/2-2bc²/2+c³/2+a²c/2-2c²a/2

=> a³/2+a³/2+b³/2+b³/2+c³/2+c³/2+ab²/2+ab²/2 -ab²+a²b/2+a²b/2-a²b+ac²/2+ac²/2-ac²+a²c/2+ a²c/2-a²c+bc²/2+bc²/2-bc²+b²c/2+b²c/2- b²c-abc-abc-abc

=>2a³/2+2b³/2+2c³/2+2ab²/2-ab²+2a²b/2-a²b+2ac²/2-ac²+2a²c/2-a²c+2bc²/2-bc²+2b²c/2- b²c-3abc

=>a³+b³+c³+ab²-ab²+a²b-a²b+ac²-ac²+a²c-a²c+bc²-bc²+b²c-b²c-3abc

=>a³+b³+c³-3abc= LHS