Question

if a³+b³+c³=3abc then find the value (a+b+c)

Answer 1

if a³+b³+c³=3abc
then a³+b³+c³-3abc=0
then using the identity a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ac)
so we can ( a+b+c)(a²+b²+c²-ab-bc-ac)=0
so we can say a+b+c = 0

hope it helps
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Answer 2

Given equation is $a^3+b^3+c^3=3abc$

To find :

The value of  a+b+c.

Solution :

From the given equation $a^3+b^3+c^3=3abc$ we may write the given equation as below

Now subtracting  " 3ab " on both the sides of the given equation we get that

$a^3+b^3+c^3-3abc=3ab-3ab$

$a^3+b^3+c^3-3abc=0$

Here by using the algebraic identity :

$a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)$

Substitute the values of the formula $a^3+b^3+c^3-3abc=0$ in we get

$(a+b+c)(a^2+b^2+c^2-ab-bc-ac)=0$

$(a+b+c)=0$ or $(a^2+b^2+c^2-ab-bc-ac)=0$

Therefore we take only $(a+b+c)=0$

The value of a+b+c is 0 if $a^3+b^3+c^3=3abc$