Question

30. Prove that
=
(a + b + c) lla - bp + (- cb +(c - aby​

Answer 1

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Answer 2

Step-by-step explanation:

$a^{3}$ + $b^{3}$ + $c^{3}$ -3abc = (a + b + c ) ( $a^{2}$ + $b^{2}$ + $c^{2}$ - ab - bc - ca)

or, $a^{3}$ + $b^{3}$ + $c^{3}$ -3abc = 1/2( a + b+ c) ($2a^{2}$ + $2b^{2}$ + $2c^{2}$ - 2ab - 2bc - 2ca)

or, $a^{3}$ + $b^{3}$ + $c^{3}$ -3abc = 1/2(a + b +c) {( $a^{2}$ - 2ab + $b^{2}$ ) + ( $b^{2}$ - 2bc +$c^{2}$) + ( $c^{2}$ - 2ca + $a^{2}$)}

or, $a^{3}$ + $b^{3}$ + $c^{3}$ -3abc = 1/2(a + b + c) {$(a - b)^{2}$ + $(b - c)^{2}$ + $(c - a)^{2}$} proved.