Question

The value of a^3 +b^3 +c^3 - 3abc if a+b+c=12 and ab+bc+ca=47 is

Answer 1

Hello, here is your answer
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a + b + c = 12 and ab + bc + ca = 47
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Now,
a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)

Again, (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

⇒ a^2 + b^2 + c^2 = (a + b + c)^2 - 2 (ab + bc + ca)

⇒ a^2 + b^2 + c^2 = (12)^2 - 2 (47) = 144 - 94 = 50

⇒a^3 + b^3 + c^3 - 3abc = (a + b + c) [a^2 + b^2 + c^2 - (ab + bc + ca)]

⇒a^3 + b^3 + c^3 - 3abc = (12) [50 - (47)]

⇒a^3 + b^3 + c^3 - 3abc = (12) [50 - (47)] = 12×(3) = 36 answer

Hope it's helpful