Value of a3 - b3 - c3 - 3abcab - bc - ca - a2 - b2 - c2- when a - -5- b - -6- c - 10 is

The correct option is A 1 As a^3+b^3+c^3 3abc=(a+b+c)[a^2+b^2+c^3 ab bc ca] ⇒a^3+b^3+c^3 3abcab+bc+ca a^2 b^2 c^2= (a+b+c) ⇒[a^3+b^3+c^3 3a ...

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Expansion of (x+y+z)^2

Value of a3...

Question

Value of $\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a b + b c + c a - a^{2} - b^{2} - c^{2}}$ , when $a = - 5, b = - 6, c = 10$ is

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Solution

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\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a b + b c + c a - a^{2} - b^{2} - c^{2}}

a = - 5, b = - 6, c = 10

\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a}

a + b + C = 12

a^{2} + b^{2} + c^{2} = 50

a b + b c + a c

a^{3} + b^{3} + c^{3} - 3 a b c

\frac{x^{3} + y^{3} + z^{3} - 3 x y z}{a^{3} + b^{3} + c^{3} - 3 a b c} \times \frac{a^{2} + b^{2} + c^{2} - a b - b c - c a}{x^{2} + y^{2} + z^{2} - x y - y z - z x}

a^{3} + 8 b^{3} + c^{3} - 6 a b c

a^{3} + b^{3} + c^{3} - 3 a b c = \frac{1}{2} (a + b + c) [{(a - b)}^{2} + {(b - c)}^{2} + {(c - a)}^{2}]

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