Question

if a+b+c=0 then show that a²(b+c)+b²(c+a)+c²(a+b)+3abc=0​

Answer 1

Answer:

See the explanation

Step-by-step explanation:

Given $a+b+c=0...(1)$

To prove : $a^2(b+c)+b^2(c+a)+c^2(a+b)+3abc=0$

LHS = $a^2(b+c)+b^2(c+a)+c^2(a+b)+3abc$

       $=a^2(-a)+b^2(-b)+c^2(-c)+3abc\\=-a^2-b^3-c^3+3abc\\=-(a^3+b^3+c^3)+3abc\\=-(3abc)+3abc\\=0$

       $=$ RHS

Since we know that $a+b+c=0\Rightarrow a^3+b^3+c^3=3abc$

Answer 2

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