Question

If ab + bc+ ca = 10 and a^2 +b^2 +c^2 = 44 find a^3 +b^3 +c^3 -3abc.

Answer 1

Answer:

(a+b+c)³=(a³+b³+c³)+3[(a+b+c)(ab+ac+bc)−abc]

(a+b+c)³ = (a³+b³+c³) + 3(10)(a+b+c) -3abc

(a³+b³+c³) - 3abc = (a+b+c)³ - 30(a+b+c)

(a³+b³+c³) - 3abc = (a+b+c) [ (a+b+c)^2 - 30 ]

(a³+b³+c³) - 3abc = (a+b+c) [ 44 +10 -30 ]

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