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    Question

    If  x = a(b - c), y = b(c – a) and z = c(a - b) ,

    find the value of  (x/a)3 + (y/b)3 + (z/c)3?
    A xy²/3abc Correct Answer Incorrect Answer
    B 3xy2ab Correct Answer Incorrect Answer
    C 3xyz/abc Correct Answer Incorrect Answer
    D xy²/abc Correct Answer Incorrect Answer

    Solution

    We know the identity a³ + b³ + c³ - 3abc = (a+b+c) (a2 + b2 + c2 – ab – bc - ca)  x = a(b - c), y = b(c - a), z = c(a - b)  x/a = b - c,  y/b = c - a, z/c = a - b  x/a + y/b + z/c = b - c + c - a + a - b = 0 According to the identity If a + b + c = 0 Then, a³ + b³ + c³ = 3abc (x/a)3 + (y/b)3 + (z/c)3 = (3xyz)/(abc)

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