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(2a-b)^3+(b-c)^3+8(c-a)^3

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(2a-b)^3+(b-c)^3+8(c-a)^3

    • Posted by Aishwarya Pradeep 4 years, 2 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Gaurav Seth 4 years, 2 months ago

    The given equation is,

     

    (2a - b)³ + (b - 2c)³ + 8(c - a)³

     

    = (2a - b)³ + (b - 2c)³ + (2c - 2a)³

     

    Let x = (2a - b) ; y = (b - 2c) ; z = (2c - 2a)

     

    Now,

     

    x + y+ z = (2a - b) + (b - 2c) + (2c - 2a) = 0

     

    Since, x + y + z = 0, then,

     

    x³ + y³ + z³ = 3xyz

     

    ⇒ (2a - b)³ + (b - 2c)³ + (2c - 2a)³ = 3(2a - b) (b - 2c) (2c - 2a)

     

    ⇒ (2a - b)³ + (b - 2c)³ + 8(c - a)³ = 6(2a - b) (b - 2c) (c - a)

     

    1Thank You

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